How do I correct variations in stain color/density?
That sounds like what we call "water marking", which is an unsightly doubling of color where the brush strokes overlap.  Typically it's what happens when you don't apply your subsequent passes of stain soon enough. Your best bet is to remove the strain with a cabinet scraper and resand. I've heard of wetting the whole area with mineral spirits first, to prevent this but I've never actually tried it myself. Just work quickly and maintain a wet edge and you should be fine, or better yet switch to gel stain which is much less susceptible to this problem.