We had our bathroom refurb recently so I've been looking into this. Here's what I've learnt (apologies for a long post 
). The fans generally fall into two main categories - ceiling mounted and wall mounted.
Ceiling mounted are usually more powerful and quieter due to the way they're are mounted - the fan itself (which is a small box) usually sits above the ceiling, e.g. in the loft space, and from the room you can see just a hole in the ceiling covered by a decorative grill (some cheaper/older models have fans mounted on the ceiling in the room, but these are ugly). Sometimes they come combined with a light. These fans need to have ducting vented outside through an external wall, roof, or eves (NOT just expelling steam into the loft space). This may be a bit tricky depending on your house configuration but it's not expensive, it's just a piece of semi-flexible plastic pipe. So generally they're suitable for a bathroom located on the top floor.
Wall mounted are usually fitted onto external wall - the fan body sits in a hole in the the wall, which goes all the way through to outside. The hole is covered by a decorative grill inside and (ideally) a louvered grill outside. The standard hole is 10cm in diameter, which is drilled using a special diamond core drill bit and a drill that can handle the load. Sounds scary but it's fairly straight forward for a person with proper tools (tradesman or a competent DIYer). I've read that wall mounted fans are generally less powerful than ceiling mounted but I guess this all depends on the model / brand.
Both types of fans can have either a dedicated switch or be wired into the light switch for the room, so the fan comes on when you turn on the light. They also may have a timer delay (i.e. the fan stays on for a certain amount of time after the lights are switched off to deal with leftover humidity / smells). Some fancier models also have a humidity sensor, so the fan will kick in when humidity in the room is over a certain level, even if the lights are not on, which may be convenient in a room with a window, but may also be annoying as they can kick in if the weather just very humid in general.
An electric fan requires an isolator switch located outside the bathroom. If it's a brand new installation, this is a certifiable work, so it needs to be installed by a NICIEC qualified electrician or by a competent person and then certified by a qualified electrician. This is a pretty standard staff, nothing complex.
Regarding sourcing - electrician may source it or you can do it yourself and he'll fit it, just discuss this with your electrician.
Regarding costs - fans range anything from £20 to £100 and beyond. Vent-Axia and Xpelair brands have a good reputation and are widely available online and in DIY/tradestores like Screwfix. Of course, there are other fancier brands, like everything else. Installation costs will depend on your location. Our electrician charged £370 for all electrics in the bathroom, but that included relocating the light switch to the outside of the room, wiring and fitting new ceiling downlighters, illuminated/heated mirror, new extractor fan, and a summer heating element for a towel rail (he didn't drill the hole in the external wall, it was done by the bathroom fitters). I guess a fan on its own would be around £100? We're in Surrey.