In theory a US citizen can visit the UK for up to 6 months, however, in reality, the majority of visitors cannot take 6 months out of their lives back home in order to stay in the UK for that long... they have jobs, they have homes, they have family, and they often can't take much time off for holidays, especially in the US where paid holiday time is minimal.
So, a regular tourist visitor will come to the UK for maybe 2 weeks, possibly up to about 4 weeks at a time. These visitors will normally not have any problems getting into the UK because they are just coming for a regular holiday and obviously have no intention of living in the UK.
But the longer someone tries to stay, the more scrutiny they will be under from UK immigration, because they may not be considered to be a genuine visitor - they may appear to be trying to 'live' in the UK on a visitor visa... especially if they are visiting a partner or a fiance (because they may be tempted to stay illegally after 6 months to be with them so they don't have to be apart).
The immigration officers will want to know things like:
- do they have a return ticket?
- do they have the funds to support themselves without working for that length of time, or will they resort to illegal working to support themselves?
- how are they able to take that much time off work to visit for 3-6 months?
- what about their home in the US, are they still paying for it while in the UK?
- how do I know they will leave after 3-6 months - what ties do they have to their home country which mean they must return?
- do they have a good UK immigration history - a number of short previous visits that show they are unlikely to overstay?
So, in general it's risky for him to come to the UK for more than about 2-4 weeks at first, especially if he has never been before, so it could be best to go for a shorter-length trip to start with. Because the longer he tries to stay, the more chance they won't believe he is a genuine visitor and may refuse him entry to the UK.
When entering the UK as a visitor, he should be able to show that he has:
- a return ticket back home
- enough money to support himself for the entire length of the trip (either in his bank account or sponsorship from you)
Ties to the US:
- a letter from his employer stating that he has been given time off to visit the UK and what date he is due back at work
- evidence of his home in the US and how he will be maintaining it while he is in the UK
- evidence of any other ties in the US that mean he must return, i.e important appointments, family members that he cares for, events he must attend etc.
Also, a good knowledge of the UK visa process is helpful too, so that he can show he knows that he must return to the US to apply for a fiance or spousal visa in the future.