Check out their web sites to know if they have children's programs, what their beliefs are, etc. Then attend for a while. You don't need an invite. Just go in, sit down, enjoy the service. Go to a few churches to get the feel of what's available in your area and who you like. If there was a denomination you attended as a child that you liked, then seek that kind of church out.
If after a while you feel that you want to be an official member (I actually waited a few years before transferring my membership from my childhood church), contact the pastor and he or she will let you know what you need to do to be member of a congregation in that denomination. If you were never baptized, you will likely need to do that first, but it's often part of the same ceremony. The pastor can tell you if you need to attend classes or anything like that. But the easy answer is - you just walk through the doors every Sunday and see if it fits and if you want to stay.
If someone approaches you, say hi. Friendly churches have greeters that welcome people.
If you want to talk to the pastor, give the church office a call, or drop them an email.
If you want to get to know people, volunteer, talk to the people in the seats around you, join a small group study.
Every church I have attended has a part of the service for offerings. Sit toward the back or middle so you can see how it goes. Look in the bulletin for when the offering will take place and simply place your money or your check in the plate. Give what you feel. If you want to be more private, see if there are envelopes in the pew to put it in first. When we had no money, there were weeks we gave nothing and there were weeks when $5 was a big deal. It's an offering, not a fine.
And if you don't know what's going on, just kind of follow people's leads. I'm so lost in Catholic mass but occasionally I go for friends' events. Nobody's kicked me out yet.
Good luck on your journey.