Getting to the ground
There are three stations in Burnley, but Manchester Road is the one you're interested if you're travelling from Leeds or Bradford. It's getting on for a 20 minute walk to/from the ground.
If driving over then there's quite a lot of street parking available - see the pub map for a couple of suggested areas. There are also some car parks if you really want to stump up a few quid and potentially get stuck for ages waiting to get out.
You need to keep clear of many of the pubs around the ground and in the town centre. However, that still leaves plenty of options. In fact, in contrast to nearby Blackburn, Burnley is a veritable oasis for the beer connoisseur. My personal recommendation would be the Bridge Bier Huis, which is around an 8 to 10 minute walk from the ground. It gets great reviews for its beer selection and is away fan friendly. It will get very busy though. If you arrive by train you may therefore prefer to try the Ministry of Ale, which is just over the road from Manchester Road station. The pub also has a great range of beers, including those from its own micro brewery. A relative newcomer is the Real Ale Factory, where the cask beers are allegedly dirt cheap! Another option, particularly if you want to take advantage of the street parking available nearby, is the Woodman. This has a decent range of very reasonably priced beers. Nearer the ground the most obvious is the cricket club next to the ground, which lets away fans in and is cheap and friendly. Close by is the KSC 110 Club which allows away fans in for a fee (a massive 20p!), and has a massive range of cask beers. Depending on where you park, the Talbot could be a good option. It goes without saying that there are a couple of Wetherspoons outlets in the town. I've no idea though whether or not they're an option for away fans.
All the pubs mentioned above, plus a few others, are marked on the pub map.
For more info on getting there, pubs, etc check out:
Football Ground Guide
Ciderspace (Yeovil Town fan site) excellent guide to Turf Moor