Bicycle Tutor

My bike is about a month old now, and about a week after I got it, I started to have problems with the chain slipping only on the 4th, 5th, and 6th gears. It is a 21-speed Magna, and I don't see any problems with the chain alignment, and there can't be wear because it is so new. I'd like to be able to fix it myself if it is possible.

What do you mean by the chain slipping? Is it changing gears? For the bike being so new, it might be good to readjust the derailleur.
See http://bicycletutor.com/adjust-rear-derailleur/

Well, it changes for a second and changes right back, so it basically makes my pedals kick and it's hard to pedal right because once it starts, it happens very frequently. But, it's only when I put pressure on it, and it is only in the gears that I mentioned above.

New bikes frequently need a tune up after being broken in. When you break a bike in you stretch the cables so everything works properly again.
Try this:
http://bicycletutor.com/tune-up/
Some of it isn't needed but this should help. My new bike was broken in and needed this after about 2 hours of riding.

I have to ride my bike to work everyday, and it is getting worse now and won't even shift to the six gear without switching right to the seventh. I haven't performed the tune up yet because i have not had time, but it is a really bad problem now.

Josh,
It's not a stiff link is it?
http://bicycletutor.com/stiff-chain-link/
-Alex

No, I just went to check and there are no stiff links.

Most likely it is just that the gear cable stretched a little. There should be a little barrel adjuster right where the gear cable goes in to the rear derailleur. If you're lucky, there's another where the cable comes out of the shifter. Try turning one of these counter clockwise ("unscrewing" it from the derail or shifter). Try maybe 1/4 or 1/2 turn at a time and try shifting again. You should see some improvement.

I should start out by saying that I'm not trying to say this to run anybody down in this thread, or to complain about anything, but just trying to relate experiences. Basically, I'm finding that you have to build in time to work on the bike when you ride, it just seems that issues always keep coming along (at least for me). If it's not oiling the chain, it's adjusting the brakes or the derailleurs, or checking out this problem or that. I'd say I've been spending about 20% of my ride time working on the bike so I could ride it 80% of the rest of the time.
Even since Christmas, I had to adjust both sets of brakes, replace the chain, check the hubs, overhaul the bottom bracket, and make an aborted attempt at replacing the rear axle (found out I ordered the wrong one), not to mention cleaning up after the old gunk I was using on the drive train when I got a bottle of Finish Line chain oil. To be fair, some of this was planned work (about 50-60% in this period), but about half of it was unplanned, but needed to be done. And even now, it sits needing the rear wheel trued, the derailleur cleaned up, and after my ride of today, which I cut short because of the problem, the rear derailleur needs adjustment (or the cable replaced, maybe both).
Basic point, issues happen.

Issues happen a lot especially if they are dept. store bikes. In 2001 I bought one from Target. Took it back. Nothing but problems. Went to Walmart and bought one there. Took it back. It left me on the trail and tuning it was near impossible. Went to a small bike shop and tried a Diamondback. that just wouldn't shift right so I left it there. Finally went to a larger bike shop and bought a demo Trek. That is the bike I ride now. It is still going strong. I've upgraded the drivetrain and shifters on it.

I agree on the low end bikes. Unfortunately, the cheaper parts just come out of adjustment constantly, wear faster, and need much more maintenance. The worst are the department store full suspension beasts. Instead of offering a decent all around bike with workable components, they push people on to junk bikes where much of the cost has gone in to cheapo suspension components that do little or nothing except add weight and complexity.
That said, I've known lots of people who buy a decent bike and proceed to thrash it. They get upset when they run it into a tree and can't believe that the derailleur bent. Part of riding well is working with the bike, not expecting to take any and all abuse you can heap on it.

I find more interesting, in this post, the discussion on new bikes, where purchased and time spend on fixing. I bought a FOCUS MB summer of 2007. I have put right about 1000 miles on it since then and I have only had to wash it and oil the chain. No adjustments of any kind until last week that I had to overhaul the rear axle, and only because I washed it and used a degreaser that slipped the gunk into the axle. I guess I have been way way lucky or I will never buy anything but FOCUS. It was always clear that I had to spend time on maintenance but it has been much less than what I planned for.
I have been looking forward to the maintenance and repair because I like working with my hands, it's cheaper than the shrink. You do get what you paid for, although I did not see in your post where you purchased and how much you paid. I have no idea what a Magna is. I do hope you develop the taste for the fixing since it actually is fun and challenging and that keeps you young.

You do get what you paid for, although I did not see in your post where you purchased and how much you paid. I have no idea what a Magna is.

Magna is one of the brands put out by Dynacraft Industries. As the site says, they deal in "Magna, Vertical, Next, and Rhino" brands along others.
http://www.dynacraftbikes.com/
Basically it's one of the department store brands that show up there - I've seen 'em usually at Target, Toys R Us, and sometimes Walmart (the Next brand). Depending on what you get and what the original sale price was, you can find some with better parts and some with worse parts, but basically you get most of the same problems as any standard X-Mart bike.

This seems to be a problem with some department store bikes. I have a Dicks Store Brand that does the same thing . Their tech cant get it adjusted out. I have an Ironhorse Maverick 1.2 and it is a great bike, no problems. It was on sale at Dicks for $200 and is rated as good as a similar TREK.