Brentford sits in west London, just south of Ealing. It owes some of it's quiet character to the lack of a tube station, but has plentiful transport links:
Railway
Brentford station (once known as Brentford Central) is on the 'Hounslow loop' of the South West Trains services, running into Waterloo Station via Clapham Junction. Weekdays there's two slow (all stations, 30 mins) and two fast (limited stop, 21 mins) trains an hour - Saturday there's just slow trains, and Sundays there's one an hour. Mon to Sat the last train back from town is around 11.48pm, which is pretty good for most things - and a little more humane than the tube.
Anglia Railways once ran a direct service from Basingstoke through to Chelmsford and beyond, stopping at Brentford. This was discontinued some months ago, due to lack of use, although Anglia admitted to me never really recovered from the post-Hatfield restrictions.
Ealing Broadway station is close enough, and offers fast services into Paddington, but also more significantly local trains to Slough, Reading and Oxford. It's often quicker (but more expensive) to travel west by first going into Paddington, the alternative being picking up intercity services in Slough or Reading.
Gunnersbury station, towards Chiswick, gives access to the forgotten North London line, which winds itself around through Willesden Junction, West Hampstead, Camden, Islington, to Hackney and beyond. Very useful, and again generally quicker (and easier) than the tube.
Check train times here.
No more than an honourable mention can be afforded to Brentford Town station, which was just north of the High St just past where it crosses the river/canal. It lay on the branch line that came down from Southall to Brentford Docks; the line now stops at the industrial estate north of the station site. Passenger services only really ran between the wars. There is occasionally talk of the Southall Steam Railway centre running trains along the branch, but I haven't heard anything for a while.
Buses
The theory that bus routes follow ley lines isn't even based on circumstantial evidence, but I'm fond of it nevertheless. Brentford is well served by bus routes:-
237 - Shepherds Bush to Hounslow Heath
267 - Hammersmith to Fulwell
65 - Ealing to Kingston
E2 - Brentford to Ealing Broadway via Northfields
E8 - Brentford to Ealing Broadway via Hanwell
Tube
As stated above, there is no Brentford tube station, but South Ealing on the Picadilly line is around a mile north, a respectable walk, or short bus or bike ride. Further north lies Ealing Broadway, on the central. Gunnersbury station is a similar distance east, and not only gives access to the North London Line, as above, but the district line.
If you're going west to Heathrow, go to Boston Manor Station - as close as South Ealing, but in zone 4 rather than 3, and therefore a cheaper journey...;-)
Minicab
If you've lived in Brentford any more than three days you'll get mincab cards through the letterbox. As everywhere, prices can vary, and I once had to give directions from the football ground to the A4, but... there's a company within South Ealing tube station, which is useful (the last 65 bus runs just after midnight).
You're unlikely to find black cabs in Brentford unless someone's been extravagant and got one here; Chiswick may be a better bet, but don't rely on it.
Cycling
How I get around, to be honest. Generally quicker than waiting for a bus for local jouneys, especially for short hops to train/tube stations. No real hills, although it's handy that the gentle slope up from the river towards Ealing is in your favour coming home at night... London cyclists will find the services of the LCC invaluable. The local group meet in Brentford lastWednesday of the moth - check with the overall body for details.
Canal
Not, alas, now a major transport method. The towpath makes a fine walk up to Hanwell or further; I once cycled up to Birmingham along the towpath (with a permit from Little Venice, naturally). A hundred years ago, however...