Mike's pretty much covered it.
But here are my rituals:
When you first buy the bike, go over it with a fine-toothed comb. Check all the fluids first; oil, brake fluid, coolant all at the correct levels? Are they clean? Are clear liquids cloudy? Are they to the correct levels? Is there wet spots around the areas you put the fluids, or where they flow to/through?
Next, put the bike in the center-stand (if it has one). Go front to back, top to bottom, just grabbing/pulling at things. Anything loose that shouldn't be? Pegs, pipes, bars, controls should all feel like they are secure, while levers should work without being 'loose' and cables should not feel like they are binding anywhere. Turn the handlebars back and forth. Do they turn smoothly, or feel like they have some play in them? If you have the bike on a center stand, does the rear wheel spin smoothly, or is the chain too tight and binding it up? When you spin the wheel, does the chain instantly turn with it, or is there some play in it first? All this stuff can tell you if you have something too loose, too tight, or have bad seals, bearings, etc...
For regular maintenance, do all of the above about once a week or so. It really only takes 10 minutes to do an inspection of your bike. As a rule of thumb, I do it every time I wash the bike. Believe it or not, the more often you ride, the longer the intervals can be between doing this. If you ride every day, things don't have a chance to bind up as much, and you'll start to feel, see, or hear if something is out of whack (though you should still go over the bike fairly regularly - I do it every 2-3 weeks, but ride almost daily). If you only ride once in a while, do it almost every ride. Things that sit for long periods of time corrode much easier.
Before every ride:
Check your tires and pressures. Are they properly inflated? Free of debris or punctures? Tread look good? Cords showing? I'm guilty of only checking pressure every couple of days, but again, I ride almost every day, and have a good feel for if something seems off.
And use the same gauge every time. Different gauges will read differently. Even if yours is off by 2 psi, it will consistently off by that amount. So if you always keep at 38psi per your gauge, using a different gauge will not guarantee your keeping the same pressure in your tires.
Also before every ride, do a quick brake check within the first hundred yards. Grab the front. Does it do it's job? How about the rear? It takes a half second, but it's good to find out before you get miles from home if you have brakes or not.
Periodic maintenance:
Inspect and lube the chain and sprockets every time you wash the bike. The more often you ride, the more often you'll need to lube. I usually lube mine once every week or so, but if I've ridden through a lot of rain, it gets done more often. The chain will stretch over time, so you will need to occasionally adjust it. Properly maintained, you can get a lot of miles out of the driveline before needing replacement. I got 15,000 miles from my last set, and that was with heavy abuse.
Oil and filter should be changed every 3-6 thousand miles, depending on personal preference. Many manufactures say their oil can go up to 7k, but I'm pretty old school, and religiously do mine at 3k. Again, check it every time you wash the bike, or once a week, whichever comes first. It should be clean and golden brown in color (just like it came out of the bottle). If it's dark and cloudy, it's time for a change.
Brake fluid should be clear, and generally very pale yellow (again, just like it came out of the bottle - though some brands can have other color to them). Normally, you don't need to change it that often. But if you look at the sight glass, and it's cloudy, dirty, or 'pee' yellow, it may be time to flush and change it. Same applies for the clutch fluid (if it's hydraulic).
Coolant doesn't normally need changed too often. Like all other fluids, check it regularly for amount and condition (yep, again, when you wash the bike). You can usually go a few seasons without changing it, though you may need to periodically top it off. If you need to top it off regularly, it may be a sign of an issue.
Brake pads should be checked for thickness periodically as well. Replacement intervals very greatly based on your riding style. Aggressive, daily riders may need to replace them a few times a year, while highway cruisers might get 3 or 4 seasons out of a set. Same goes with tires. If your tread depth is getting low, start contemplating new ones. Tire compound will also dictate intervals between replacement.
Once a year or beginning/end of riding season:
If you live somewhere where you can ride year round (SoCal, Fla, etc.) it's always riding season. But lots of us have to put the bike away for the winter. Even if you ride year round, you should contemplate a once a year routine similar to what we do to prep for winter/spring.
I do a full oil change before riding in the spring. The bikes been sitting for months, and oil naturally deteriorates over time, even when just sitting.
Pull the spark plugs. If needed, replace them. But inspect them as well. They can tell you a lot about how your bike is running. Are you running too rich, too lean? Something else going on?
The plugs will tell you a lot.
Check and replace (or clean) all your filters. The oil filter gets done with changes, but many people neglect air and fuel filters. If clogged or dirty, they can rob you of a lot of performance.
If your actually storing the bike for the winter, put a full tank of gas in it and add Seafoam, Stabil, or other fuel stabilized/cleaner to it. An empty tank allows corrosion on to possibly set in on the inside of the tank. If you have a petcock, shut the fuel off, and drain the carbs. Gas that sits too long (especially untreated) turns to varnish over time, and gums up every thing.
Buy a cable luber, and lube all the mechanical cables. Throttle mainly these days, but many older bike also use cables for clutch and brakes. All cables stretch over time, but if kept lubed, they'll last much longer.
And of course, wash the bike, doing your normal maintenance routine.
If you notice, for me at least, much of my maintenance and inspection of the bike revolves around cleaning it. It really is the perfect time, since your already bending over, getting into nooks and crannies. It's real easy to do, and only adds a few extra minutes to the process. Plus, it's easier to spot things when the bike is being cleaned. Stubborn, sticky dirt around seals, bearings, lines or gaskets could be an indication of a leak. You can tell if something needs tightened if it seems loose as you wash it with the sponge. Or whatever....
The other thing about doing all this simple, regular maintenance, is it can prevent, or warn you of, potential problems. Having to constantly top off a fluid means you may have a leak somewhere, or a gasket or seal going. Inconsistent tire pressure can warn of a small puncture, or that you may be into the cords. All kinds of things can be caught with regular maintenance, instead of seemingly popping up out of nowhere while you out in the middle of a ride.
I'm sure I've missed some things. But you've got the basics now.
