You do actually need to go to www.lta.org.uk
and become an LTA member - if you're a member of a British tennis club you can join for free. Once you have received confirmation of your membership you can begin to enter tournaments - the list of available tournaments can be found if you click on the 'Search' button at the top right of the LTA's homepage. Some tournaments can be entered online however for most you will have to contact the tournament organiser either by phone or email to get entrance details - there is generally a charge for entering the tournament. Grade 1 tournaments are actually the highest quality of tournament and will consist of the best players. You are entitled to enter most tournaments [although some required a rating of 4.1, 3.1 etc or higher - your rating, i.e ability level, can be gained from your club's coach and then entered online or you can be given a suggested rating by the LTA website] and your best bet is contact the tournament organiser and to ask about eligibility.
There is no connection between LTA ranking/rating and gaining access to Futures tournaments however the standard is often very high at such tournaments and an average club player would get little more than 6-0 6-0 - although this shouldn't necessarily stop you from trying! If you do decided to enter Futures tournaments[Satellites are now defunct..] you will need to get an 'IPIN' from www.itftennis.com
. This will then allow you to enter into Futures tournaments. However as you will start as an 'Unranked' player you cannot enter tournaments online and will have to simply turn up on the day of qualifying at any Futures tournament with your IPIN to hand.
If you have any more questions, just ask.. I'll answer to the best of my knowledge!