The first thing you need to descide is wether you want to assemble your own skateboard, or buy one that has already been put together (called a "complete"). Either way is fine. It's just up to you. If you are a new skater, you might as well get a Complete.
But you'll still need to know what dimentions you want your skateboard to be. This is where a lot of skaters get lost. Don't worry! It's a lot easier than it sounds. Here's a little secret - for your first skateboard, getting the right size and shape is almost impossible. That's becasue as a new skater, you really don't know WHAT you want! That's OK - but I can tell you general sizes to go by. Read the article "Build Your Own Pro Grade Skateboard" - it gives general guidelines for the sizes and brands to look for. Then, once you know what sizes you want, you can go to a skate shop or to an online skate store, and pick out a skateboard that fits as closely as you can to what you picked out! It's that easy.
If you want to build your own skateboard, then you can just buy the parts that match what you picked out, and put it all together. Or you can ask someone at the shop to assemble it for you. They should be able to easily.
Buying a complete skateboard is usually the easiest way to go if you are a new skater, but let me warn you - the real danger isn't in getting a skateboard that's a little off of the right size or shape for you. That's not a big problem at all. The real danger is when you get a complete skateboard that's mostly poor quality junk. There are plenty of these out there, like land mines set for unsuspecting parents and kids. Only, instead of hurting you now, they end up hurting you or your kids later. They are often sold in superstores like Walmart or some large sporting goods store. Now, not all cheaper complete skateboards are junk ... but it can be tough to tell. Read this FAQ on buying cheap skateboards for more help in deciding if a cheaper board you see in the store is OK to buy.
For some suggestions on brands of complete skateboards to buy, you can check out these two articles: Buying Complete Skateboards and Buying Beginner Skateboards for Kids. Both articles will yell at you about not buying cheap complete boards, which by now I hope I've expressed my opinion of that option clearly enough! Otherwise, they'll give you some ideas for buying complete skateboards.
Whatever you end up buying, keep in mind that it will break. Skateboarding is tough on skateboards. Decks break. That's just how things work. So, whichever way you go, complete or building your own, either way you are going to have to maintain your skateboard later. That's fine, and normal - so don't worry if you don't think your board is nice enough, and don't spend too much on parts that you'll have to replace!