So, Nemmonis, you let loose a fire bolt that singes the skeleton. Would anybody else like to act?

FYI, this is called the surprise round of combat. If no creatures have noticed you and you want to attack them , the players group get 1 free turn, during which the enemies cannot react to or take against against the players. This is basically the time to really load damage on to the enemies before actual combat begins. You can move and take actions as usual. but the enemies can't.

I move towards the zombie at a quick pace and it was with the intention of attacking this zombie.

I want to attack with my shortsword.

Ok, with your shortsword, I assume. Roll attack for me, and damage. Easier to put it in one post rather than 2 lol. :)

(Do I add a modifier?)

On your character sheet, under Actions, it should show you your weapons, along with attack modifiers, and damage. You shortsword has a +5 modifier to its attack roll, and does 1d6+3 damage. 

7 - Attack

7 - Damage

I follow the Goliath and throw my dart at the Zombie, aiming for its eye. (what do i roll for this with the attack roll, dexterity?)

Eglig, you swing your sword at the zombie and narrowly miss. 

Nico, you would add a +3 to your roll. Dex + your proficiency bonus of 2. 1d4+1 for damage

9 (Attack)

4 (Damage)

_____________S_______        ______________________

________________________________________________

________________FFFFFFFF______________________

________________FFFFFFFF______E_Z_____________

________________________________________________

________________________________Ni______________

________________________________________________

____________________        ________________________

                                  Ne D 

                                      M

Ni= Nico, Ne= Nemmonis, D= Durk, E= Eglig M=Maidens Z= Zombie F= Fountain S=Skeleton

Nico, your dart goes wide and clatters harmlessly to the ground behind the zombie. Durk, are you going to do anything?

i cast bardic inspiration on Eglig

Ok. Now, everyone needs to roll initiative to determine the order of combat. Your initiative is shown on your character sheet.

Zombie: 13

Skeleton: 3

3

5

Inititive: 5

10

So the order is: Zombie, Nico, Nemmonis, Durk, Skeleton, Eglig.

The zombie is going to try a slam attack on Eglig.

Attack: 12

Damage:4

(Hits for 2 damage)

Ok, it is now Nico's turn