Okay, it’s a simple job if you're experienced on the spanners. But if you're staring out, it might seem like a massive, scary task. Removing your own wheels will save you cash on otherwise straightforward tasks – getting new tyres fitted being the biggie. Take your loose wheels to the tyre shop in the car and they'll often fit your new tyres for free. Getting them fitted to a bike can cost up to an hour's labour: pricey nowadays.
You'll need to buy some kit, paddock stands being the main thing (assuming your bike doesn’t have a centre stand). But the tools and stands will make a load of other jobs easier – new brake pads, chain adjustment/replacement, oil changes etc etc. So, look on it as an investment for the future!
Make sure you have plenty of room to work: tidy up the garage, and if you're working outside, check the weather forecast to make sure you'll be spannering in the dry.
Sort out the tools you'll need: socket or spanners to fit the front and rear axles, (and often a giant hex bit for the front axle), Allen bits or sockets for the caliper mounting bolts, axle clamp bolts on the front forks, chain adjusters at the rear. You may need to loosen the front mudguard to get enough clearance to get the front wheel out too. A torque wrench is a good idea for these big fasteners too: we don't want anything coming loose round here.
Get the paddock stands ready – but before you put the bike on them, it's worth loosening the axle nuts. They'll be tight, and it's sometimes better to take the initial torque off when the bike is on the ground, rather than on the (usually less stable) paddock stands. Remember to loosen any axle clamp bolts first (normally on the front fork bottoms), and remove any split pins or R-clips on the spindles.