Most tennis players start playing tennis at School. Most schools will have equipment and courts to play on during the summer. The best way to start learning is at school as it doesn't cost you anything.
If after playing at school you decide this is something you want to pursue then this is the time to invest in a racquet. To start with it doesn't need to be the best most expensive racquet just something that lets you play whilst you learn the basics.
Some schools will have after school tennis clubs. If not they may still let you play on the courts after hours, you just need someone to play against. If you can't find someone to play against try playing against a wall to work on your shots.
Head down to your local library and find a book on tennis. Read the instructions and with the book practice your strokes even if it is without a ball in your own room just get use to the motions.
Watch as much tennis on TV as possible. Study what different types of players do and find a style that suits you. Try and add this to your game when your next on the court.
Find as many different people to play against as possible as if you only ever play against one player you're not going to improve.
Talk to your PE teachers and see if your school competes in local or national competitions and ask if you can be put forward. Check if your school is a member of the BSTA (BritishSchool's Tennis Association) if they aren't tell them to join.
Enquire with your local leisure centre and see if they have any tennis facilities and if any clubs use them. Find out when the local club uses them and go down and introduce yourself. Leisure Centre's also normally let you hire racquets so if you don't want to buy a racquet it is a good way to play.
Get in touch with your local LTA (Lawn Tennis Association) their details can be found by going to www.lta.org.uk. They will be able to tell you everything that is happening with tennis in your area and nationally.
As with every sport you have to be in good physical shape as well as good at the game so build some exercise routines in to your week to build your cardio-vascular and muscle development.
Once you have progressed through the ranks and are starting to get some local media attention try contacting companies for sponsorship towards your equipment and travel costs.