Greetings, I will, in a while, do a step by step. However there are here on BYC some very good examples of this type of incubator, except for size and exact placement of certain items, they differ little. 
For use with less than half dozen eggs you won't need one this size. This chest is nearly 36" long.
After studing here on BYC for a while and/or when you are ready and gathering what you need to build, ask the members who you see working with Homemade what to use for this or how did they do that. 
When you are ready I will be more than happy to help as would most others.
For a dozen or less I would use a insulated box or case close to 24" long it will be at least 12" OD wide. Get that and we'll tell you what else you need. If you're like some of us you have most of what you need tucked away.
You asked: Where do the chicks go after they hatch"? They go into a brooder. First things first.
Good luck! I'm glad you like what you see.
Richard