You can find many riding schools and Equestrian Centres that offer lessons to beginners in your local area. To do this, you can use the BHS Riding School locator here. You can also undertake searches on your prefered Search Engine (Google, Bing, Yahoo etc) for riding schools and Equestrian Centres near you.
Most of the time, you will only need some shoes with a small heel as hats are usually provided by the establishment for beginners (sometimes a small fee applies). It would be advisable to take some comfortable trousers with you as riding in jeans can be uncomfortable and result in chaffing. Leggings or tracksuit bottoms would be ideal as well as a T-Shirt, a jacket can also be worn if necessary but this must be zipped up to stop it flapping. More information can be found in the Clothes for the Rider section here.
Usually for the first couple of lessons you will be on something known as "leadrein" where a worker at the establishment will walk around with you and help you understand what the instructor is asking you to do. They will usually stay with you until they think you are ready to ride by yourself.
A group lesson is when you share the menage with others that are also there to have a lesson. Therefore, you all have an equal amount of time getting advice and hints off the instructor. A private lesson means you have the menage to yourself and the instructor will be concentrating on you and only you, however this tends to be much more expensive.
You will usually find that these types of horses are the safest as they have been specially trained to be used to learn to ride. There may be the odd stubborn one but riding school horses are usually 99% bombproof.
You will usually learn how to mount, dismount, walk, trot and canter. To go further such as jumping, you may have to book special lessons if that specific establishment caters for that type of work. Some establishment also offer services such as "Own a Pony for a day" that gives you an idea of what it's like to look after and care for a pony. These usually including grooming, riding, turning out, mucking out, lunch and turning in.
You can check if you're on the right diagonal whilst trotting by looking at the leg closest to the wall (outside). The easiest way to remember this is the saying "Rise and fall with the leg on the wall" which means rise when the outside leg comes forward and sit as it goes backwards. Another way to remember is when cantering, it's the front leg that should be the leading leg, so most people remember them as "Opposites".
You can achieve this by giving a gentle squeeze with your legs. Sometimes, a horse will refuse to listen to this so you may have to squeeze harder or even carry a crop with you as usually even the sight is enough to urge your horse forward.
This can be achieved in a number of ways but the usual way is to ask whilst trotting. More advanced riders can get their horse to canter at a walk or even at a standstill but the way we ask always remains the same. You move the leg closer to the centre of the school (inside) slightly back (behind the girth) whilst keeping your outside leg where it is and you give a gentle squeeze. Again, just like trotting, if your horse decides it doesn't want to listen to your leg you may have to squeeze harder or carry a crop.