Websites: The internet is awash with amazing websites that cover a great deal of unsigned music; Next2Shine, The Dutch Guy, A Higher Revelation, When The Grammarphone Rings, Hype Machine and House In The Sand and are just a few of them.
Streaming Services: Streaming Services give you on-demand access to virtually every bit of music that's being produced currently, so there's unparalleled access to unsigned artists. Be sure to look at the suggestions SoundCloud gives you (or just go exploring) as well as what Spotify plays on their 'Radio' and 'recommends feature; some unsigned goodness is sure to crop up.
Festivals: Whilst you're going to have plenty of artists on your list that you're keen to see, festivals are the best place to discover acts you never knew before so take advantage. As you have a wander during the day, make an effort to swing by some of the smaller stages to see if anything takes your fancy - especially the BBC Introducing Stage and anywhere playing the best of local talent.
Radio: We all know the best shows to listen to in order to find the hottest current thing but did you know that many major stations have good shows dedicated to unsigned artists? XFM have their X-Posure show and Absolute have their Sunday Night Music Club, hosting new music and unsigned band reviews with Sarah Campion. BBC 6 Music are known to champion the underdog whenever they can too - espcially Tom Robinson, Steve Lamaqc, RadMac and John Peel's son, Tom Ravenscroft. As well as major stations, there's always the wonderful Amazing Radio which exclusively new or unsigned talent.
BBC Introducing: The fantastic BBC Introducing program has given birth to many superstars such as Florence and the Machine, Jake Bugg and George Ezra. They've got a stage at many of the major festivals, so be sure to check out a few acts on there; you're bound to stumble across someone impressive. They also have several shows on mainstream radio, such as 'BBC Introducing with Jen and Ally' on Radio 1.
Venues/Nights: Well going out is of course the best way to discover new talent! If you go out and see unsigned artists play, you'll definitely know if they're any good or not. In London, be sure to head to White Heat at Madame Jojo's and Old Blue Last in Shoreditch. Both venues often host unsigned or new artists that soon get shot into fame. The Well in Leeds has a history for putting on a range of quality unsigned bands no matter what the genre and Green Door Store in Brighton put on similar events. The Social, The Maze and Spanky's in Nottingham are a good shout too - but a quick Google will tell you wherever the best venue for local music is in your area.