Use the best equipment possible. A good microphone is essential especially for sounds. If you don't want to buy it, maybe you can rent it.
You can do a lot with sound processing, but you can't turn a crappy recording into a good one. Try to create good recordings, it will pay later.
Best mic for sound FX is a condensor mic with a large membrane. I got one for 350 €, which was a bargain. You need a pre-amplifier with that, or an interface which provides 48V phantome voltage. Pre-amplifying is also good for recording those tiny little sounds like clothes rustling etc., also it provides some low cut filter for eliminating deep frequencies (like the sound of your feet).
Recording interfaces are cheap nowadays, and even the cheapest should have a better sound quality than your PC's soundcard.
Alternatively you could invest into a HD recorder, especially if you want to go outside for recording. I'm going to buy this one
http://www.zoom.co.jp/english/products/h4n/ for 350 € because it covers nearly all of my needs. I was especially searching for different mic jacks, this one has it all: XLR, 7,5 and 3,5mm. XLR cables have best sound quality (audible only if the other equipment is up to that standard).
Other devices like Minidisc recorders could be good enough as well, depending on your needs. I have had bad experiences with MP3 recorders and don't recommend those. Remember that until 1990 all field recording was done on magnetic tape, which still is good enough for general purpose. Nowadays the only problem would be to get a machine in good working condition.
You should always place the mic as far away from your PC as possible. Best would be a recording booth or a different room. Use some dampening. I hang blankets all over the room, and an extra thick one between PC and mic. This way I get virtually no PC fan noises, and I create a "dry" recording which is always best.
Voices should be recorded at a distance of about 20 cm from mouth to mic, longer if louder (for screaming). With condensor mics the sound of a voice changes with the distance, experiment a bit.
Get a good recording by setting the correct level: no distortions, but loud enough. Always normalise your recordings before doing anything else. If necessary, use a noise gate on voices. Don't overdo it with cleaning up sounds, as much of the background noise gets covered in the mix, notably if you use some continuous atmosphere sound.
Listen to your recordings with a good pair of speakers. Headphones are good for recording and for exact cuts, but not for judging general sound quality.