A ripple carry adder is the most simple and easy to understand adder so new people listen up cause this tutorial will show you all the basics and things you need to know!
Now before we get into the adder you first have to know about logic gates (xor in particular) Les has a in depth tutorial for logic gates so I will put up the truth tables for some logic gates.
https://www.realdigital.org/img/228d4788d26e286b5706f6d644ddee8b.svg
If you do not know what a truth table is then listen here. It is a Table that represents all possible inputs and outputs from circuits and gates.
Now you know logic gates lets get into adders.
I will first show you 1 bit of one of the most simple ripple carry adders and explain in depth how it works.
The xor gate will be light blue wool and the carry will be yellow wool.
Btw an xor gate looks like this in minecraft.
fyi the torch on the right tip of the xor is an and for the carry in the adder.
So what does a 1 bit full RCA adder look like?
Well it looks like this:
If you dont understand any of that here is a little video of me explaining it 
https://vimeo.com/638336327
Hopefully this guide helped you if you have any problems feel free to reply to this.