Fights where no one moves are boring. I’m relatively new to DMing and ran into this issue a couple times. It also happens sometimes in our campaign where I’m a player.

What do you do to get everyone moving around the battlefield? Any simple tips or tricks that can be applied during the creation process of an encounter?

Probably the surest way is to give the whole party a mobile target, and minions that WANT to hold them in place. The captain has the Maguffn, and if he gets away the terrorists win.

Another sure way is to use enemies that can blink, or misty step, or ethereal jaunt.

You can also add some terrain:  a tree to hide behind, a ledge to climb/jump off of,  a barrel of oil that could explode, a ditch or small chasm.

Also, enemies with AoE attacks will make the party move :)

Mostly, you need to create a reason to move. The big ones are generally cover (moving so you have cover from specific enemies, or so enemies don't have cover from you), needing to engage, and damaging zones.

A rolling boulder once inspired Indiana Jones to move a bit.

Thanks for the suggestions. I do like the idea of a mountainside battle with boulders being a factor. Going to have to be really conscious of how I build battlefields I suppose.

Only trick I can think of that hasn't been mentioned is to have enemies that actually move the players as well. A caster could use a thunderclap that has added knockback, an evil druid could use thornwhip to drag a player closer, an ogre could smash a player and send them flying or even throw them. 

I was designing combats for a while where the players would pretty much know what they were up against ahead of time, and be able to fine-tune their strategy to the point that they rarely had to re-evaluate mid-combat. I think having characters reveal abilities on the second or third round of combat, or having reinforcements come from an unexpected direction also encourages players to move around more. 

I've had the same issue. Could throwing in a rogue or two on the "enemy-team" help? The ability to disengage as a BA and then move at least gives you as a DM the opportunity to move some of your NPC's without provoking opportunity attacks. Same actually goes with the hide option. Might also make it easier to make obstacles "matter" since it creates some more movement. Just an idea, I've never tried it, but now I might :-)

yeah, i'm going to have to be very thoughtful with my obstacles. I think the rogue thing is a good idea. I think I may just move my baddies more in general and just take the opportunity attacks regardless.

Quote from CozmoTheGrey >>

yeah, i'm going to have to be very thoughtful with my obstacles. I think the rogue thing is a good idea. I think I may just move my baddies more in general and just take the opportunity attacks regardless.

 Well, only move them if they have a reason to move. My experience is that a lot of positioning has to do with things like optimizing cones, close cubes (e.g. Thunderwave), and lines.

Area of Effects are great motivators.  Oh look, 80% of the party wants to gang up on the something, a couple of AoE's will teach them it is better to take a single AoO than have multiples of them get hit by an AoE.

Don't forget folks can move IN threatened space as much as they want, they don't provoke AoE until they leave the space normally.

Want to watch your party split like ants while being as mobile as possible? High level monk with the mobile feat, who shadow steps in a dark temple along with some minor henchmen, spread out. Combine this with the monks naturally terrifying unarmed damage combined with their ki points for extra flavor in any manner you see fit. Assume the monk is intelligent and tactical, and have him pick on the weakest members first (like the hollow-knight does) and have him keep a high level of self-preservation, to where he seems to have a fear of confronting the party tank (usually the most immobile of all). You will watch the spellcasters rush to try to stay close to someone (dear god anyone) and the tank begin chasing down and searching for the monk whenever he disappears to drink his health potion. Suddenly, the party has never felt safer running around, trying to keep eyes on the monk, to stop him from simply constantly running up, taking his attacks, and then bonus action shadowstepping out of sight.

You can make the terrain move if the players won’t. Rising water, spreading fire, a tree falls down, a sinkhole opens, a pillar falls down, and some ceiling with it, a deer charges across the battlefield, a tornado, a landslide, an earthquake. Something that creates a zone that effects both sides. A group of civilians can be fun to mess with AoE spells and force casters to move into better positions. 
That’s actually a kind of thing I like to do when someone rolls a 1. Not a critical fumble, but a battlefield event where something random happens that changes things for everyone. (Full disclosure, I stole the idea from an old DM)

Goblins by default can disengage and hide both as a BA, definitely a good way to keep things mobile

You could use timed trap with basic sequence to force movement. Like this turn black tiles became hole, next white have spear falling from the ceiling...

Provide actions on specific tiles like a rope to release some light from the top. Something to do or remove to activate or cancel.

Timed informations like a burning paper during the fight to force them to reach it before consumption. Depending the delay they could have less information.

Move your creature so they add to regroup to protect the squishy wizard.

However opportunity attacks are made to restrict movements.

Pf2e does a better job than 5e at getting people to move. Due to 5e's core rules melee is very disincentivised  to move and movement is often neutralised by the movement of the other part  but  there are ways to get people moving in 5e

1. Break movement equality. By default most monsters have the same movement which they get for free without sacrificing combat effectiveness.  If it becomes unequal because one is faster  or slower then the  net 0 movement balance of combat is broken. If the faster side can push that advantage with ranged attacks or free disengages then movement becomes a good strategy
2. Locational advantages/ disadvantages.  By default all tiles are essentially equal but you can assign them different advantages and disadvantages. This can be damage/healing, cover, varying visibility, flanking, short range attack disadvantage, spell effects or forced movement. Players/monsters will tend to move to the best position they can access without sacrificing attack opportunities and stay there so if you want to keep people moving then the advantages/ disadvantages need to move.  Also keep in mind forced movement is rare so don't expect players forcing enemies in to areas of disadvantage to be common.  
3. Forced movement. While forced movement exists in 5e it is often limited to special abilities or involves sacrificing damage. If you make these effects more common for players and monsters then controlling enemy location becomes a larger factor and amplifies the importance of movement to locational advantage/disadvantage. 
4. Trading movement for attack power.  One of the reasons pf2e has more movement is that movement and attacks use the same resource. This means that if you make an enemy move it makes less/weaker attacks.  This incentivises the weaker party to  move to try to force the stronger enemies to move and hence loose attack power.  5e doesn't have this baked in like PF2E does but you can  create abilities that have similar effects. If you give a monster a powerful melee or short range attack they can only use if they don't move then players are incentivised to move away to make  it  move and prevent that attack. In 5e this isn't expected so you will need to telegraph it to make it obvious. An example of such an ability would be the rogues steady aim, it give the large sneak attack boost and advantage at the cost of movement.  If the rogue was melee only then enemies would be incentivised to move away to prevent that ability working. 
5. Make opportunity attacks rare and promote movement.  In 5e players are often afraid to move because attacks of opportunity are the default and have consistent triggers.  Without them players would be more willing to move and if triggers like casting spells or making attacks were more common then they may make it more of a priority to move before taking those actions.  If you make most monsters not have attacks of oppurtunity and make it so that it's more common for them to trigger on things other than movement then movement will be more incentivised.  For example in pf2e only professional fighters like soldiers have attacks of opportunity that trigger on movement  but they also trigger on spell casting and players can still cast spells after disengaging. This means casters usually move away from such enemies.  You can get a similar effect  in DnD by making it so attacks of opportunity trigger on spell casting and range attacks but not movement e.g mage slayer and sentinel.
6. Diverse objectives.  Most of the weaknesses of movement in DnD rely on the assumption that the goal is to hit more attacks than the enemy but that doesn't need to be the goal of combat.  You can add objectives that require movement for example getting to a certain place, escaping an enemy or  going to a location to pass a skill check  in order to incentivise movement outside of the typical combat structure. 

The floor is lava.

I like this suggestion the most. Are of Effect (AOE) damage is king of the battlefield. 

One cool thing is too have an enemy immune to a damage type, like a Red Dragon immune to fire damage. When players gang up on them in melee, activate something like a Wall of Fire spell, or a pillar of fire in a certain area. Movement = avoiding damage. 

However, the opposite is also true. Can create an AOE buff. A temporary area that gives some buff (AC boost, add 1d4 on attacks, add 1d6 temporary hit points, etc.). Players will be motivated to get to those areas and gain the benefit. 

This is kind of a joke, but kind of brilliant. 

A crumbling floor, where beneath it... the floor is lava. 

You could do something like every round, 5 feet of the floor falls out. Or random sections of the ground erupt with lava as the volcano gets ready to blow. 

I use battlemaps often and one memorable fight was in a cave with many stalactites and stalagmites. The enemies could hide behind cover and or knock stalactites down upon the party. The safe area was where a stalactite already fell. But the shattered stalactite made the area difficult terrain.

Another similar battle I just dropped pieces of paper from a height to symbolize chunks of ice falling from the sky. The paper showed where the ice was going to land on initiative 0.