You could use a milk crate as a nest box and be fine. I have one of mine that refuses to use a nest box and always lays in the same corner of the coop. A minimum of a cubic ft for the nest box.The roost should be higher than the nest box because they want to sleep as high as they can get.
You definitely need a nest box unless you have two roosters lol - otherwise they will build themselves a nest and it will likely be hidden or hard to get too. They want to lay eggs somewhere they feel safe.
There are A LOT of different ways to go about it depending on your style of coop. You can look in the coop design section for some ideas.
I have 5 chickens with two nest boxes on one end of my small coop and roosts on the other. It is all made out of wood and very simple. People get really creative and also use buckets and ladders and all sorts of things. Knowing more about your coop would help. Here is mine:
A nest box opening form the top needs to be an exterior one. For that you need to make a box out of plywood or boards and 2x2 or something like that coming out and when you are attaching the top board/plywood, just put it on hinges where it attaches to the back, you can probably see alot of examples in the coops section or pictures of others' coop.
For perches, use any things you have like a broom stick, a small branch, handrail, or even a 2x2, 2x3 or 2x4. You can just screw it in to a wall or make supports to hold it out away form a wall or form the floor. Also alot of pictures in people coop threads.