I realise that this can be expensive, but a lesson even once a month is beneficial. Your instructor can assess you and you horse together and spend time helping you to bond and improve. You really need to work your horse in an area measuring 20 by 40 metres, as this is the size of a standard dressage arena. If marking your own arena out is impossible, consider hiring a local yard's. Of course, if your own yard has a school, this will not be a problem.
Most people start their career doing unaffiliated dressage.
Your local riding club may run competitions, or know somewhere that does. The equestrian press is full of competitions to go to. You can try dressage then at low cost to yourself, and see if you and your horse enjoy it. Eventually, you may want to affiliate. This means joining British Dressage, gaining points for your horse and upgrading the standard you compete at.