I would always recommend puppy classes, not only for training purposes but also socialisation - good basic training will generally cure most of the problems people have with dogs, before they even become a problem. Never force your pup to do something, patience will pay off... forcing them will only create a nervous pup and subsequently a nervous adult dog.
If you would like to be able to show off your achievements in training your dog, you could enter the Kennel Club's Good Citizen Training Scheme, where you and your dog can earn certificates for different levels of obedience and are great fun.
If you would like to get into Agility, Agility Net is a good place to start.
Lead Training
This is an important thing to get right from the start... the result of not getting it right could be a fully grown dog who pulls like a train. Putting a lead on a pup for the first time can be daunting for your pup, try first putting a lead on in the back garden and just let the pup pull it round behind them. When you start to hold the lead do not put any tension on it, follow your pup around the garden just loosely holdin the lead. Make the lead a nice friendly thing without over exciting your pup when you get your lead out. When you start to walk your pup, he/she will want to be near you anyway so shouldn't feel the need to keep tugging you, so again, allow the lead to be there, just in case, but without tension, if pup starts looking interested in something else or in a different direction to where you're heading, call his/her name to get their attention and carry on walking in the direction you were headed. Teaching your dog to heel, with and without a lead will stop any pulling issues before they start.
Recall (Come)
Teaching your pup to come to you when called is THE most important thing you can teach him/her. This is done really easily. Sitting on the floor with them, distract them and get them to walk away from you, by throwing a toy etc - only a small distance, then when they are already on their way back to you, say "Come" or call their name in a friendly and excitable manner - you could also buy a whistle and peep several times on it. Only say it once, then when pup returns, give him/her lots of fuss and say good boy/girl. Repeat this only a few times in one session. Two small sessions of this per day and your pup will have learned recall in no time. As your pup gets older, the sessions can be longer and you will need to practice this in the garden next, then when out on a walk, I would suggest keeping your pup on a long line/extending lead until you have mastered the 'come' command.
Sit
Show your pup a small treat that you have in your fingertips, then raise it slightly up and slightly back, this should encourage your pup into a sit position, if this doesn't get your pup into a sit position, keep trying, eventually the pup will have no choice but to sit down. You can gently try to encourage their bottom down with your other hand, but do not force them into a sit. With patience and time, this will work for you. If you are using a clicker; have it in the other hand, click as soon as the puppy's bottom hits the floor and then give the treat. Puppies are clumsy with taking things from your hand at first, so you may have to place it in their mouth initially. Alternatively you could do all of the above and a short peep on a whistle when they sit.
Down
Once you have mastered sit you can start training down. From a sitting position show your pup the treat you have in your finger tips and slowly move it down to the floor, again you may need to do this several times before your pup lays down, but it will work eventually. Again if you are using a clicker, click as soon as they are in a down position, then reward..
Spin
This may seem like an odd thing to teach your pup... however - on wet days if your dog can come into the house onto a towel you just happened to put inside the door, they can spin on it to get some of the mud/water off. To teach this, show your pup the treat, then slowly move it around the pup to get the dog to do a 360degree turn, as soon as they're back where they started, click and reward.