First, if you're just replacing pads, you're not opening the system and don't necessarily have to bleed it. But this is a great opportunity to flush your system (should be done every year, actually) so go for it! If you have symptoms of a mushy brake pedal, insistent braking performance (the car may pull to one side or another during a hard stop), or you experience "brake fade" (you have to push harder and harder while stopping at a given rate) you should bleed the brakes.
To bleed brakes the old fashioned way you need a buddy, brake fluid (your system is not compatible with DOT5 fluid-- any other grade is fine), a wrench or socket for the bleeder screws, a length of rubber hose, and a clear glass container. I suggest glass b/c brake fluid can eat through most other materials-- but anything you can see through will work.
Top off the master cylinder reservoir. Put a box-end wrench or preferrably a 6-point socket onto the first bleed screw and just break it loose. Don't take a shortcut and attempt to use an open end wrench. Now attach the hose to the screw and put the other end in the bottom of your container.
Put a wrench on the screw and doublecheck it's snug. The torque spec is low-- do not go gorilla on a bleeder screw. Now have your assistant pump the brake pedal 3 times. Hold the pedal down at the end of the 3rd pump. Now you will open the bleeder screw until air comes bubbling out of the rubber hose. Your assistant's foot will hit the floor. Leave it there until you snug the screw again (to prevent air from getting sucked back into the system). Repeat until clean fluid w/ no bubbles is coming out of the hose. Periodically check the master cylinder and top it off to ensure it never goes dry!
On a non-ABS car, the bleed order is pretty simple. Just start on the longest line and continue down to the shortest. This means right rear, left rear, right front, left front.
Brake fluid removes automotive paint so clean up any spill quickly.
One more tip. Brake fluid absorbs water which is a bad thing as water boils at a relatively low temp. Once you open a bottle of fluid it begins sucking moisture out of the air and will eventually go bad. So buy your fluid in the pint containers and only open what you need. Toss the remaining fluid from the open container when you're done. Brake fluid is a hazardous substance and must be disposed of according to local regulations.
I'm glad you're doing this yourself. Especially on non-ABS cars, brake maintenance is most often very simple and requires very few tools. You can save a ton of money! -scott