Here are some train times, with fares as at 06/11:

Leeds	0740	0816	0847	0915					Kew Bridge	1657	1715	1727
Wakefield W	-	0829	0901	0928					Vauxhall	1720	1741*	1750
Kings Cross	0950	1030	1100	1130					Kings Cross	1803	1818	1818	1833	1903	1933
Vauxhall	1026	1056	1126	1156	1326	1340	1356		Wakefield W	2006	2023	2023	2037	2059	2130
Kew Bridge	1050	1120	1150	1220	1350	1408*	1420		Leeds	2021	2041	2041	2052	2116	2145
Single fare (to Kings Cross)	£65.30	£68.20	£68.20	£68.20					Single fare (from Kings Cross)	£47.80	£31.20	£31.20	£33.30	£43.80	£40.80

 * Change at Clapham Junction
 
Fares from Leeds (italics means can be bought on the day):

Notes:
1. Use trainsplit.com to find the cheapest deals available by splitting your journey; don't buy tickets from them though, use www.tpexpress.co.uk or www.lner.co.uk.
2. Railcard holders get one third off the above prices.
3. Groups of three or more can get approx 20% off East Coast Advance Singles fares if booked at www.lner.co.uk.
 
There are no trains from Sheffield to St Pancras because of engineering work. Travelling to/from Kings Cross can be done from £63.50.
 
If you don't mind spending most of the day on a coach, you can do it for around 25 quid return from Leeds, or 20 from Sheffield with National Express.

Getting to the ground
The ground is about a mile east of Brentford's previous ground, Griffin Park. They've somehow managed to shoehorn it into a space that's not big enough for a football ground! Kew Bridge station is basically next to it. It's fairly easy to get there from Kings Cross. The quuickest way is probably to take the Victoria line to Vauxhall and then an overground train. These run every 30 minutes, and the total journey time is 50 minutes if you hit it right at Vauxhall. However, there are additional services from/to Vauxhall, changing at Clapham Junction. Alternatively you can head for Gunnersbury (from 45 minutes journey time, 10 minutes from the ground), Acton Town (35 minutes on the Piccadilly line, a good 20-25 minutes to the ground), or Chiswick Park (Victoria Line to Victoria or Piccadilly line to Hammersith, then District line, again a good 20 minutes to the ground). The advantage Chiswick Park has over Acton Town is that there are pubs between there and the ground. After the game away fans are "discouraged" from using Kew Bridge station. Access post-game is via an underpass from Lionel Road South. Away fans aren't allowed to walk around the ground to get to the queue, but have to go "the long way round", by which time the queue will be massive. I therefore suggest heading straight to Gunnersbury or Acton Town, from where there are tubes every couple of minutes. Gunnersbury is closed for an hour after the match.
 
Driving there isn't much of an option. There is very limited official parking, which must be pre-booked here. The two car parks, one next to the ground and the other a 20 minute walk away, are both expensive and situated within London's Ultra Low Emission Zone, so that's big chunk of money unless your car is exempt. Street parking is basically not an option anywhere near the ground because it's all restricted to permit holders.

Pubs
The new ground is nothing like as good for pubs as Griffin Park was. There are options though. The most obvious is the Express Tavern, which is more or less outside Kew Bridge station. It looks decent enough, and is marginally less expensive than most of the others. A bit further south, there's the One Over the Ait, the Steam Packet and the Bell and Crown on the north riverbank, and the Cricketers and the Greyhound. These are all upmarket establishments with eye watering prices, and all but the Bell and Crown don't open until 12. If you arrive at Chiswick Park or Gunnersbury you might want to check out the Gunnersbury or the Pilot. The former would be my recommendation.
 
I haven't read anything to say that any of these pubs don't allow away fans in or are to be avoided. Apparently many of the hard-core Brentford fans still drink in the pubs around Griffin Park
 
Pub map
Kings Cross pub map
Brentford FC stadium guide
Away fan info (from Brenford FC)
tfl travel latest
Beesotted (good unofficial site)
Football Ground Guide
London Transport