It's very good that you are both somewhat socially awkward in that you will understand each other's hesitations and lack of knowledge in the area of dating and being with others. It could easily work very well for you two.

I would ask you first, do you hang out with this person already or do things with him?

I would bring it up casually as just doing stuff together. It does not need to be a formal "date" as in dinner and a movie kind of thing but can just be hanging out at the mall or something similar. Being together hanging out and getting to know one another is a good start. Don't make a grand production out of it. I am going to guess that if you try to make a huge deal out of it, it will not only make you nervous and anxious but also he might be affected the same way.

Just ask him "hey wanna go to ______ together sometime?" or something like that maybe?