Burnley is located at Junction 10 of the M65. Rail links are adequate rather than particularly impressive. The Blackpool North to York Northern Line train stops at Burnley Manchester Road station. The very efficient X43 bus service runs from Nelson to Manchester at regular intervals. There are also National Express coaches from as far afield as London that drop off at the station.
Taxi ranks are everywhere, both London cabs and independents. Expect to pay more in the London style cabbies, and make sure you agree the price at the independents, as they are not averse to trying to rip you off, especially if you're obviously out of town and/or drunk. Prices are mainly reasonable, though.