What is there to do?
The scale of the programme will vary depending on the size of the con. For a typical weekend con, the programme will start at about 19:00 on the Friday, and finish at about 18:00 on Sunday. At any given time, there may be multiple events happening simultaneously, especially at larger conventions. Some major events, such as the Guest Of Honour speeches, will probably not have anything scheduled against them.
Some conventions, especially smaller ones, may arrange gaps in the programme around mealtimes, but larger British cons usually don't bother. I am informed that gaps for meals are common at U.S. conventions.
The actual events will vary from the serious to the downright silly. There will be single-speaker talks, panel discussions on various subjects, silly games, quizzes, and several other things I haven't thought of. Some items will concentrate on a specific work of written fiction/area of science/TV programme, but most tend to cover more generic themes.
In many cases, many programme items will share a common theme, often related to one or more of the GOHs. For example, the 2002 Eastercon had several programme items concentrating on aspects of Alternate History, since the one of the Guests of Honour was Harry Turtledove, who has written many alternate history novels.
The convention committee will often issue a draft programme before the convention, either in the final progress report or via a web site, which should give you some idea of what to expect.
The Dealers' Room
Several specialist SF/Fantasy booksellers, both new and second-hand, together with dealers of other fannish items, who will gladly sell you their wares.
A perennial favourite. Lounge around, consume your beverage of choice and discuss varied subjects with other attendees.
Note to readers in the USA: I am informed that many US cons have no alcohol on-site, so things can be a bit different over there.
Help Run the Convention
Many cons are run entirely by volunteers. While the big jobs are taken by the time the con happens, there's often a need for Gophers to help things along. So what's a Gopher? Sort of a general dogsbody, tasked with running errands to help the con go more smoothly. Things like fetching drinks for speakers in panel items, finding said speakers before the event when the organisers have lost them, any any other odd jobs that need doing. The name comes from the ubiquitous phrase "can you go for..."