Ah, the finer points of tuning a snare drum! This takes some practice to get it right, but here are the steps:

After the bottom head is on & tuned, turn off the snare strainer (where's that plug again?) and loosen the "snare tension adjustment screw" just before it detaches.

If you've got string or cord that connects the snares and snare strainer, you've got a little tougher job. Let me say first that you can't use just any old string - it just isn't strong enough. Tennis racket string works well, but doesn't tie very easily. I'd try to use some type of nylon string instead - you can get a foot or so at a hardware store for less than a dollar. Cord tends to stretch, so I'd encourage you to start with the snare strainer OFF and tie down then ends (remember that as you pull it tight, the strainer has a tendency to turn itself back on). After you get the ends fastened, turn the snare strainer on, then off again. Chances are that the cord stretched, so tighten the snare tension screw some and turn the snares on again.

If you forgot to loosen the thumb screw before you started this whole process, you're going to have to start over! Most problems with bad snare drum tuning are caused by a strainer that is "maxed out" and leaves no more room for adjustment.

Final Adjustments - Tighten the snare tension adjustment screw until you reach the desired sound. I like to start with a loose "wet" snare, then gradually tighten while I play SOFT taps on the drum. When the snares are stretched too tight, you won't hear them vibrate (resulting in a "choked" snare sound). If you make the adjustment while playing loud strokes, there's a good chance that you'll tighten too much - then your snare drum will sound like a tenor drum at soft dynamic levels!

Turn off the snares & listen to the sound of your drum. If you've got overly "loose" drum heads, you'll hear a drum that rings a little after you play it. If you don't like that ring, you've got a couple of choices: either tighten the bottom and top head until the drum doesn't ring - or, if you like a "lower-pitched" snare sound: you can put a muffling patch on the drum.
     There are several different commercial muffling systems available - most of which you can make at almost no cost! As you start making big bucks off your newly found talent, I'm sure that you can afford to buy the most expensive stuff out there, but for MY budget, here are a couple of alternatives:.
     Take an old drum head that fits on the drum and cut out an inch-wide strip from around the outside edge. Lay that "donut" on the drum & you've got an instant "deadringer." You might want to put a small piece of tape on it to hold it in place.

Even cheaper alternative:.
     Take a small piece of cotton cloth or Kleenex and tape it to the batter head. The amount of muffling you use will depend on the size of drum & what type of sound that you want to achieve. I personally like a piece that's a couple of inches square for the snare and mid-toms, maybe two patches for the floor tom. Usually the mid-toms and snare don't require any muffling on the bottom head. The bass drum usually requires much more - maybe a small pillow or blanket that partially rests against the batter head inside the drum..
     Don't make the mistake of OVER MUFFLING! I hear drums that sound like cardboard boxes all the time - what a waste of money! Usually if there is NO RING, it might sound good where you're sitting - but walk a few yards away & you'll hear what I'm talking about. Experiment by having a friend play while you listen! There's no 'right' answer - use your ears.

The short answer is to put a pillow or blanket inside the drum, but before I make every drummer in the world mad at me, let me say this:

It depends on what type of sound that you want from your bass drum (have I said that enough times?). If you're looking for a "thump," then that solution will work AS LONG AS YOU DON'T WANT THE VOLUME. Realise that most of the volume and 'carrying power' comes from the drum's resonance - you take away the resonance (or 'ring'), you take away the power. Experiment - use a smaller blanket or pillow. Have it resting on the batter head, then not. Remember, just because it sounds good to YOU, doesn't mean it sounds great to the audience!