I wish I could attach some pictures, but I haven't a working camera at the moment. I will look for some helpful links, meanwhile try to explain in a bit more detail and more clearly.
I neglected to suggest that the very first thing I do with a garment that I believe needs alteration is wash and dry it (or wash and re-block it, if it's a sweater), just as you would do for a pair of too-loose jeans. Many times this will solve the problem, especially if I have bought off the rack and others have tried the thing on and stretched it. This alone will solve the problem about 50% of the time.
Making darts in the back of a neckline will make the neckline narrower, which has the result of raising it in front as well as making the shoulders slightly narrower. If you make two - 1/4" darts in the back of a neckline, its total circumference will decrease by a total of 1". This will affect the front as well as the back of the neckline, and also (very slightly) narrow the shoulders. 1/4" to 1/3" darts are about as large as I can make without screwing up the way the garment fits in other areas. So the effect from this alteration is much more subtle than taking a couple of inches off too-long tank top straps.
Sometimes I run across situations where, because of the nature of the fabric or the style of the garment, I can't make the alteration I prefer. And I do not love to sew enough to be willing to start deconstructing the garment to make truly professional alterations. I would describe both the neckline dart thing and the strap cutting thing as quick 'n dirty solutions. Most of the things I've altered this way are light, inexpensive summerwear that I may have for a season or two. If you are talking about an expensive piece you hope to wear for years, I'd take it to a seamstress or tailor.
I will search for some sewing tutorials I can link; meanwhile if you are really interested in doing this, ask a friend who sews how to go about it. It's much easier to understand if you have a real-life demo, for sure.