For some reason the paladin in the game I’m running wants me to create a subclass for him based on dental hygiene. He’s a newer player who I don’t really trust so I told him I would do it except I’ve never actually home brewed anything before and I don’t really know how to make it balanced so if any of you could give me some tips or suggestions that would be great

I played with someone that made a homebrew plaque knight as a monster and it was just creepy. 

I would say take one of the other official subclasses and look at changing its features to match the feel you're wanting. Look through al spells to see if there is something that fits the theme for a paladin oath spell. As long as you stay close to the power levels at each point, you should be ok.

I’m going to second Mairondil‘s suggestion. Pick a subclass you have access to that is similar to what you want and use it as a template. 

I agree that the best idea is to take one of the existing Subclasses, and change it a bit to be Dental-based. I'm picturing this as someone who has such perfect, pristine, shining white teeth that it actually helps them with their charisma and such. So with that in mind, I'd say Oath of Glory is a good starting point.

I would swap Peerless Athlete (where you can use a your channel divinity and a bonus action to get advantage on Ahletics/acrobatics, plus a few other things) with... let's say "Peerless Smile", which same basic idea... CD+BA and instead you get advantage on Charisma checks for 10 minutes.

Keep the other Channel Divinity, "Inspiring Smite", change the name to "Inspiring Smile", and have it do the exact same thing (bonus action to give out Temp HP to allies).

7th level Aura of Alacrity doesn't totally work with the Dental theme, since it's a speed boost for you and allies. I think instead you could swap it for something like... "Aura of Hygiene". Soemthing like:

"You emanate an aura of cleanliness and Hygiene. You and any allies within 10 feet of you have resistance to Poison Damage and immunity to the Poisoned Condition. In addition, clothing worn by you or allies within your aura cannot become dirty.

When you reach 18th level in this class, the range of the aura increases to 30 feet."

Super basic, but it feeds into the idea of dentistry more than the default subclass feature.

At level 15, Glorious Defense works fine as-is... just reflavor it as being a shining, gleaming grin that temporarily blinds enemies long enough to give allies a temp AC boost.

Same with the 20th level feature... just give it a goofy dental-themed name and otherwise use the exact some functions.

Thank you all for your advice this was super helpful and I will be sure to try this stuff at the next session.

Healthy Mouth is a Healthy Life. Before one can help others, one has to take care of themselves by ensuring they follow a healthy lifestyle, including rigorous dental hygiene.

Winning Smile. Your smile is your greatest asset, combat is only a secondary option if charisma and confidence fails to reach a constructive compromise.

Fight Decay. Toxicity, decay, and filth will slowly destroy society from the inside, you are committed to finding it and routing it out just as you protect your own teeth.

Oath Spells:
3rd : Charm Person, Detect Poison and Disease 
5th : Magic Mouth, Spiritual Weapon
9th : Blinding Smite, Tongues
13th : Aura of Purity, Grasping Vine
17th : Animate Objects, Wall of Stone

Channel Divinity
3rd level
Winning Smile As a bonus action you grant yourself advantage on Charisma checks for the next minute.

Bad Breath As an action you release a cloud of poison in a 60ft cone, each creature must make a Constitution saving throw against your spell DC, on a failure they are poisoned for 1 minute. Affected creatures can repeat the save at the end of each turn ending the effect on a success.

Aura of Brilliance
7th level
When a creature within 10 ft of you attacks you, you can flash your brilliant teeth at them. Using your reaction you can impose disadvantage on their attack roll. You can use this feature a number of times equal to your Charisma modifier, you regain all uses when you finish a long rest.

Rinse
15th level
If you start your turn paralyzed, stunned, poisoned, frightened, charmed, petrified, or blinded, you can instantly end one of the effects imposing that condition. Once you have used this feature you cannot use it again until you finish a long rest, unless you expend a spell slot of 2nd level or higher to use it again.

Pinnacle of Hygiene
20th level
As a bonus action, you can empower yourself with the power of your perfect teeth. You gain the following benefits:
- You are immune to being grappled or restrained.
- You gain a +10 bonus to all Charisma checks and Charisma saving throws
- Hostile creatures that start their turn within 10 ft of you take 5 radiant damage.
- You have advantage on Constitution saving throws

These bonuses last for 1 minute. Once you use this feature you cannot use it again until you finish a long rest.

Awesome! I love the selection of Oath Spells... I don't know what it was, but I started laughing at the idea of getting Magic Mouth, since it's so thematically appropriate. I feel like the only ability that feels off is Bad Breath... it feels counterintuitive to the hygiene-focused features of the rest of the subclass.

Maybe you could just have it do cold damage and call it "Minty Fresh Breath"... maybe reduce their speed for a turn.

Ooh yes! that's better. I thought a breath themed one would be fun, but drew a blank for hygiene.