If you're on quite a bit of a budget and you're making hip hop music (I assume you are, judging from your grammar and sig), then I'd suggest purchasing some cheap multitracker (n-Track or similar, make sure it is VSTi compatable) and then download a few free drum synths from kvraudio.com. Then do a hell of a lot of reading on recording. It may seem like a simple thing at first, but it's really frustrating when you go to record some music and it turns out sounding like crap. And then you realize you need to spend mucho $$ to make it sound better. Welcome to the mess we're all in
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To answer your question bluntly..........no. A mixer does not, has not, and will never be able to make "beats". By beats I assume you mean everything except the vocal track. A lot of people use Fruity Loops (or now it's called FLStudio), but if you're not willing to lay down the money for it just yet, then the n-Track/drumsynth/softsynth method works as well, but it's not as easy to make a decent sounding song. You're music will sound more creative with n-Track because you're actually making the sounds, and making the beats, rather than using a bunch of pre-recorded samples. If you want to spend a lot of time researching, then I highly suggest using n-Track ($50), a drum synth (a couple are free), and some softsynths or samples (some are free). Then all you'll need is a mic and mic-pre for the vocals and you're set. For info on mics, just look around here, and 95% of your questions will be answered. People hate it when they see the same question posted multiple times, so do a bit of work first, so as to not get on people's bad side.
I've just recently doven into the electronic music scene from my traditional rock (all types). I'm starting to make hardcore stuff, so while I do know SOME stuff about synths and drum synths, I know very little. The folks over at KVRaudio.com know 3 million times more than I do, so definately go check them out.
I will answer your soundcard question because I'm in a very informative mood right now. A soundcard is an electronical device that is usually found in a PCI slot on the back of your computer. The purpose of the soundcard is to transfer sound to your computer and back. Most computers come with a built-in soundcard which is NOT made for recording (because the quality is just plain bad, but you should be able to manage for a little while with no new soundcard). The card is actually built onto the motherboard of the computer and is accessed by three 1/8" holes. These holes will usually be green, blue, and pink in color and labelled as headphones, line in, and mic in, respectively. When you get your mixer, you will want to connect the outs to an RCA->stereo 1/8" adapter (radioshack has them) and then to your soundcard's line in (blue). Your mic will plug into the mixer (which has a built-in preamp).
I will not provide a step-by-step guide for you and I will not answer every question you have. I am not a teacher, and a good thing that is, because I get very impatient very quickly. Please, try to work stuff out on your own, look at old posts, read the manuals, and do a little bit of work. I know, it sucks, but no one is going to want to hold your hand every little step of the way, and almost everyone will get annoyed if you constantly ask questions that have been answered already. Let this be a warning to you.
Good luck on all your future recordings! And welcome to the boards.
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GOOD LORD HE/SHE IS ONLY 14 
