Most Efficient Way to tune rear gears of mountain bike I have a schwinn ranger suntour mountain bike which I enjoy riding and ride frequently.  When the bike was new I had no difficulty shifting through all 21 speeds of the bicycle with 3 gears by the crank and 7 by the rear wheel.  I can shift through the 3 gear speeds with no issue, however currently  when I attempt to shift to any of my rear 7 gears nothing usually happens I appear to be stuck around 2nd or 3rd gear no matter which gear is selected and I am noticing more frequent chain slipping.  

The amount of slack for the cable for the derailleur for those gears can be adjusted by loosening a screw with an alan wrench, it is currently loose on my bicycle (I haven't been riding around like that)

Is it possible to regain access the rest of my gears and reduce chain slipping?
What is the proper technique to resolve this issue of gear shifting?
Generally, if you haven't bent the derailleur (or its hanger) [such as by having a crash], you should have been using the barrel adjuster as shown in this image 

 

(from here)

in order to make tweaks to the adjustments. The mis-adjustment you were experiencing was likely just "cable stretch" in the non-bent case. The barrel adjuster changes the cable tension, which you were more drastically doing by undoing the bolt which holds the cable (so you may have put wrong cable tension now). From the description, it sounds like you don't have cable tension (and thus the shifters can't pull anything and shift).

The rest of the adjustment options (screws) change the derailleur limits (big and small cog) and angle of the derailleur (b-tension). These should be set-it-and-forget-it (unless the derailleur gets banged up, in which case it must be un-banged up and then possibly re-adjusted). 

Park Tool has a good description on how to adjust a derailleur, which you should read and implement (or take the bike to your LBS, give the guy 5 bucks and get him to adjust your derailleur and check if its bent). If the derailleur/hanger is bent, it must be un-bent prior to adjustment. 

Another thing that may be occurring (though unlikely) is excess cable friction in which case the shift cable+housing need replacement.