Once your screen is all prepped its time to put that puppy on the press. I've found it a lot easier if I put whatever I'm aside so I can see the platen, then put my screen in the hinges. Unless you buy a premade press, hinges are crucial, because you can bolt these puppies onto just about anything, and they clamp down well so your screen doesn't move. It's helpful if you draw a line in the center of your platen from the front to the back, then lay the screen down and align it to the center. Placement of the screen between back and front kind of depends on what you are printing; you just need to judge what that for yourself, there is no one solution for everything.
If you are doing multi-color work here is a quick run down of how to tackle it. Do you first color, and put down a test print and cure it. Swing around your second color/screen and align that screen to first print. This sounds easy in words, but can prove very difficult pending on how well you completed your prior steps and what resolution of artwork you're dealing with.

Once you get your screen placed it's time to tape it off, I personally cover the entire area of the screen without artwork in tape. This is because it's better to waste a few cents in tape than screw up a print. Here's what my screen looks like all taped off. A tip to conserve tape and energy: If you put multiple pieces of artwork on your screen then tape around all of them, then apply patches of tape over the parts you don't currently want to print. After you print with one area and you're ready to print another piece of artwork on the same screen, clean the ink out then tape the underside of the screen so you don't accidentally transfer ink from one print to another. Also a note on tapes, not all tapes are created equally you must find one that resists ink, does not leave a residue when you take it off, and it's nice if it tears easily so you can tape your screens quickly.

Printing

Now the big moment, finally putting your artwork on the substrate! So break out your choice color of ink and put it just before your negative; don't skimp, but don't pour out a gallon. First rule, do a test print or you will make your life miserable. Test on anything, preferably scrap that is as close to the material you want to do your prints on. Once you are thoroughly happy with how you're artwork prints onto your test then go right into printing the rest of your materials. There are many things to consider while printing, everything from how hard you should pull your squeegee and how many passes you should do so. The best thing you can do to get good at this is to practice, practice and a bit more practice. If you feel uncomfortable printing then you can always try talking/watch some pro screen printers in your area, most small screen print shops are happy show a little bit (especially when you approach them like you may want their services).

Techniques

I'm going to try and cover as much as I can to help you with text, but still the best way to learn sometimes is to fail. One that will help and comes with a bit of practice is making your pull with the squeegee smooth as possibly, if you get hung up this causes uneven pressure and sometimes a bad print. A good habit to always do it only pull the squeegee one way, towards you from back to front of the screen, this may seem obvious but in some cases it can be tempting to deviate; if you do you can more easily lose registration.

Flooding: There are a few techniques that you can use when printing, one of my favorites is flooding the screen to do this build up a bit of ink to pull towards, and drag the squeegee towards at a very steep angle so you don't push much ink through the screen. What this accomplishes is it put a fairly even coat of ink over the printing area, and then gives it a good solid pull through and you should get a pretty even print. There is one more reason to flood your screen, when you are using air-dry inks you should flood the screen in between each time you change out the item you are printing, this prevents ink from drying in your screen.

Pinholes: If you find you missed a pin hole earlier on, a quick way to fix that is to put a little piece of tape on the underside of the screen where the hole is.

Mass Printing: Another thing to keep in mind is if you happen to be printing larger volumes of materials, be very cautious of every movement you make as you will be printing for quite awhile. Conserve your movements and get make the process as efficient as possible.

Base Layer: Let me elaborate, say you're printing white ink on a black shirt naturally this is not going to be as easy as printing black on white. So what you do is put down a layer of white ink, and take a heat gun and set the ink(in the commercial world you use a flash). Then you can print right on top of the first layer of ink to make an even brighter white. You can use this same technique to make colors more vibrant on black (or any darker color), put down a white base layer then print the color and then print the color on top.

Curing the ink

Curing the ink is setting it so it is permanent. Okay, even if you set the ink on the press with a heat gun you still need to cure it. Unless you have access to a belt dryer, I'd recommend using the oven. Yes, baking your shirt will make the ink last longer. I've found that 1-2 minutes @ 400°F works pretty well. Be careful, you can burn your shirt (especially whites) and potentially cause a fire. If you do not cure your shirts then you will probably notice ink fall off within a few washes.