Speed up Windows
Back in the "good old days", when Windows 98 was cutting edge, we were used to it: in time, Windows became mysteriously slower and more sluggish in reaction. Not much to be done about that then, but now, with Windows XP being today's standard, we shouldn't just take that anymore as a given fate.
But before we start, some background info. If your computer slows down, that is because something uses up it's resources. The keys here are processor power, memory and network bandwidth.
Running applications and data is loaded from the hard disk into memory, so it can be accessed quickly. But what if the memory is full? Then Windows starts "swapping", which means it writes stuff back to the hard disk to free up some memory. Pretty much like you writing down a shopping list

Then, when the "swapped" data is needed again (because you just clicked on the still open Word window you haven't been using for a while),
it has to be read back from the hard disk to memory. Sticking with our example, that would be you searching your pockets from that shopping list. That takes a while (in both cases, mostly

).
So how about processor power? Well, it's a "computer" after all, so it needs to compute stuff all the time. If your processor is very busy, either because it's an outdated model or some application requires all its attention, the computer's reaction to your urgent request of opening Word is slowed down.
Network bandwidth is the speed your network (e.g. Internet) connection is working. If you have a lot of traffic going on, that website you want to open is taking a while to load. Just like in real life, huh?
So, now you've bought a nice new computer a while ago, and now it's all slow in reaction, what to do about that? Well, first we have to find out what's exactly the problem. A useful tool for that is the Windows task manager. Right-click on the taskbar and open the task manager. In the "performance" tab, you have two interesting graphs: the current processor usage on top and the current memory usage below.
The most common case: you're running out of memory. You have 256 MB memory build-in, but task manager shows you that you're using 400 MB already. So Windows spends a considerable time already swapping stuff to the disk and reading it back again. Where's all the memory gone? Have a look at your open windows first. Do you really need that large powerpoint presentation that has been open for a while right now, or can you just close it first to free up some memory? Also have a look at the system tray. That's the little section in the bottom right corner, where the clock is showing. Do you see a lot of symbols there? These are all little applications running in the background. Go through them and check if you really need them all to run all the time. Like, there's Real player. How many times are you listening to real music files? Just occasionally? Then throw it out, it'll start fast enough when you need it. The same is true for many of these little "helper" applications. Often, you can disable them right there, by right-clicking on the tray symbol and unchecking something like "load on startup".
Also have a look at your startup folder. You find it under start -> program files -> startup. Whatever is there will be loaded when Windows is starting. Do you need all that stuff? If some are not needed all the time, you can delete the link there. Don't worry, it'll not delete the software itself, just the link in the startup folder will be gone.
When you're done with that, reboot your computer. Check the task manager again to see if you have more memory available now.
If something is using up your processor power and you don't know why, task manager is also your friend. Have a look at the processes tab, there's a column "CPU usage". You can sort it by clicking on the caption. There, you see which process is using how much of your computing performance. Now you'll have to find out from the process name which application that is. If you're not sure of it's too cryptic, try to google for it to get some info on what it is and how to stop it from being hyperactive.
Finally to network performance: That's a more difficult one, not so easy to analyze. If your internet connection is slow, it can have far too many reasons to have general advice on that. One thing you should do first, though, is: Have your virus scanner installed and up-to-date. Probably it's time to let it run a full system scan. I can also recommend you a free tool to check for some unwanted applications that sneaked into your computer and are now using up your network performance: have a look at http://www.lavasoft.com, their program is easy to use and free for personal use.
That's it for today folks! Hope I could help you a bit.