1. Forget About Ollying
This is probably the biggest mistake the kids in my road make - trying to run before they can walk, so to speak. You've got no chance of being able to ollie until you are completely and utterly comfortable with riding around on your skateboard.
2. Set Up Your Skateboard
Get your skateboard sorted out. If you don't know what the different bits of your skateboard are called then start here and read from there.
As a beginner, the chances are that the one you've got is pretty slow, with Abec 'A' bearings and a thick, heavy deck. Your deck won't have much concave (meaning it won't be very curved) but the good news is that this type of board is less likely to slip away from you so in fact is ideal to learn on.
I would not recommend buying an expensive skateboard at first. Firstly, good skateboards are surprisingly expensive, and if you end up not wanting to skateboard buying one is going to be a waste of money. Secondly, they are a lot faster which makes them harder to ride and less forgiving.
One thing you probably need to do is loosen your trucks because new skateboards tend to have them done up very tightly. Although this is very stable, you won't be able to turn your skateboard at all and if there is a natural lean to the board (as there usually is) you won't be able to correct this while pushing off, so you'll end up riding in to a wall or whatever all the time. To loosen your trucks, simply unscrew your kingpin a few times so that the board is easier to turn. Some kingpins need an alan key and some need a star shaped screwdriver. If you don't have the tools, any skateshop should be happy to do this for you free of charge.
3. Work Out Your Stance
Some things you need to work out straight away - whether you are regular or goofy, and whether you are a 'mongo foot'. Stand on the skateboard in the most comfortable way for you and then imagine pushing off. If you don't know the definitions, look them up in the tricktionary -
The tricktionary is my extensive guide to skateboarding trick names and terms. Knowing the correct lingo before you start will make it easier in future to understand trick tips, articles and so on.
If you are a mongo foot, now is the time to teach yourself to push properly before it becomes too natural for you. There are actual technical reasons why it's bad to push mongo footed - it takes longer to setup for tricks, you are less stable when pushing off (because your weight is behind the skateboard) and beside this mongo footed skaters look awkward and unstylish on their boards.
4. Push Off
Start pushing off up a shallow hill or on a level surface. I have noticed that the beginners have a couple of common problems. Firstly, the skateboard tends to get away from them as they are pushing, because they tend to push from a position where their feet are level with each other or even with the pushing foot behind the front foot. Instead, you should imagine that pushing off is like walking - your pushing foot must step in front of the foot on the skateboard and then push back, just like taking normal steps. Your front foot should be just behind the front bolts.
Secondly, the action of pushing off should be a smooth, powerful movement, not a short, stuttering one. Most of the beginners tend to take about ten small pushes before getting on the skateboard, when a couple of long, smooth pushes will gain the same speed. Most skateboards also have a lean to them which makes them turn one way or the other. While you are pushing off try to use your foot on the skateboard to lean the board one way or the other so it doesn't turn.
Getting on requires you to twist your foot that's on the board around to face sideways instead of forwards and step backwards onto the back fishtail. Make sure you step on firmly and confidently and don't mess about as this is when you are most vulnerable to falling off. Your feet should be behind the bolts in both cases, so if you don't get into this position straight away, try to quickly shuffle into the correct position. Many beginners step their back foot either in front or on top of the bolts, and if you do this you must step back onto the fishtail quickly otherwise the skateboard is difficult to control.
A Stable Riding Stance
For the first few times just ride out the skateboard until it stops, but soon you should get used to pushing more before you run out of speed. Again, this needs to be done confidently, as if you hang about there is every chance the skateboard will slip out from you as you are only riding on one foot.
When you've got some decent pace just practice gently leaning the skateboard to turn left and right. You don't need to physically lean your body, but just put more of your weight into your heels or toes.
After a while try lifting the front wheels briefly as you lean to get a sharper turn. Do this by applying a bit more weight to the back tail until the front wheels are off the ground, then aim the nose a bit more towards whichever direction you are facing and put the front wheels back down again. Do this repeatedly while you turn to turn in as tight a circle as possible.
There are quite a few ways to stop on a skateboard, but most of them are quite advanced - things like powerslides and 'boneless' stops will be covered later.
The obvious way for a beginner is what's known as a tailstop. This is where you grind the tail of the skateboard into the ground, letting the friction slow you down. It works pretty well, although it's not very efficient if you're going really fast. You will also wear away the tail of your skateboard - personally I don't mind this, but you might, depending on how precious you are about the board. Put it this way - it will take a hell of a lot of tailstops to wear the board down entirely, by which point you almost certainly will want a different one anyway.
Another technique is to do a sort of 'reverse push' - where you use your pushing foot to slow yourself down gradually by taking small steps onto the ground that push against the direction of travel. Although again this isn't that great when you're going really fast. In those situations you should probably just jump off and worry about what happens to the skateboard later!
Turning also slows you down.
My advice is to use tailstops. Even though it wears your board out, it is a useful 'trick' to learn because it's a start towards practicing your balance. When you first do one, you're going to need the confidence to stomp the back down quite firmly and then ride out the tailstop at an unfamiliar angle (with the nose in the air) until you come to a halt. While you are doing this, try turning at the same time as well. All these little things will add up and be very useful later on.