I will be going there for a visit this summer and staying for about 4 months as a tourist but doing it like that you don't have to show any documentation about supporting yourself unless you are talking about the fiance visa then yes, you will have to show that.
Actually, if you are coming to the UK as a visitor for 4 months (a long period of time), you will need to show a lot of evidence to prove you are a genuine visitor and are not trying to live in the UK without a visa.
You will need to be able to show:
- a return ticket
- bank statements showing you have enough money to support yourself in the UK for 4 months without working in any capacity
- a job to return to in the US (a letter from your employer stating that you have been given time off to visit the UK, and what date you are expected to return to work)
- a home to return to in the US (i.e. evidence of homeownership/mortgage payments or evidence of an ongoing lease in the US and that you will be continuing to pay rent while in the UK).
- any other ties to return to in the US that mean you must go back and will not be tempted to stay in the UK (i.e. family to get back to, important commitments that you must not miss)
The Immigration Officer at the UK airport will be expecting you to be able to prove that you are a genuine tourist and that you have no intention of trying to live or work in the UK illegally.
If it's your first ever visit to the UK, it might be safer to come for a shorter period of time on this trip (maybe 2-4 weeks), so you can start building up a positive immigration history with the UK. Then you can try a longer trip after you have been here on a shorter visit or two.