If you want to get yourself out there, you're going to have to spend money. You should be able to get a cheap microphone for about £20 and with that and you're laptop, you'll be able to make a couple of demo recordings. There are plenty of books or Internet articles around about how to achieve good recordings using microphones and how to mix the songs properly.
Once you've got your CD, write all your contact details on it. Venues receive loads of demo CDs and they may lose the case or the details that came with the CD. If you write your contact details on the CD, it will increase your chances a lot. Send your CD with a 'Press Kit' which is, at least, a piece of paper with your contact details and a biography about who you are, what sort of music you play, your influences, experiences and a couple of photos.
Send your demo CD and Press Kit to whichever venues play your style of music. Clubs, bars, coffee shops, fairs, librairies, festivals, house parties...... You could also consider signing to an agency who will have lots of contacts in the music business but this can get expensive. My advice would be to avoid agencies until you have started to make a name for yourself and are making a bit of money from your music.
The most important thing you can do is to network and promote yourself. If you haven't got a mySpace profile for your music, get one and upload the demos you've made. The more information you put on there, the better. Keep checking and adding friends so build up your profile and name. The more time and effort you put in, the more you'll get back at the end of the day. Making friends with other musicians can only be a good thing. Even if they don't play the same music as you, they could always ask you to play with them or recommend you to a venue. As the saying goes; It's all about who you know, not what you know.
Good luck