Congrats on your decision! I'm sure members will be along soon to guide you! In the meantime, check out our little resource guide, put together over the years by members frequenting this forum. It can be easy to miss on the front page of the forum, so here is a link.
By the way if you find any bad links let me know. THe guide was created a bit of time ago!
If you want to adopt a non-infant child domestically, getting approved by your state's child services adoption program is your first step. You'll have to take some training classes and do a bunch of paperwork. The requirements differ by state, but Googling "YourState adoption from foster care" should pull up the right website.
35 is no problem, and single mom is no problem.
Congratulations on your decision to adopt.