Visitor Visa to Marriage Visa?

I came over to the Uk back in March on a visitor visa.  I would like to stay and it seems to me the only way is if her and I get married.  I have looked everywhere and get tons of conflicting info.

Bottom line...

1. She is a British Citizen (born and raised)
2. I am American here on a tourist visa
3. I would like to stay in the UK with her.
4. Neither of us are afraid to get married
5. What, if any, steps do I take to accomplish this as quickly as possible?

You can't get married and stay here.  One way or the other you will need to return to the US to change your status. 

And if you don't leave before your 6 months are up, it will only make it more difficult and complicated. Are you both over 21?

Depending on when you arrived in March, your six months should be coming to an end quite soon.  You need to get a ticket back to the US and then figure out the marriage plans.

You have two real options here, considering your visa could run out any day.

You can 1. return to the US apply for a fiancée visa, return and get married in the UK within 6 months and when you are married apply for your FLR which will let you work

Or 2. You and your gf can return to the US together, get married, apply for your spousal visa and return as a spouse directly which allows you to work from the start.