Trick 1: use longer than usual headers, put 'em in from the back side. If they're not quite long enough, press down on the plastic part so that there is none of the pin left sticking out the bottom, then solder.
Trick 2: solder them in upside down, with the plastic up in the air. When finished soldering, shove the plastic down to the board.
Trick 3: put the headers on the back side of the board. If you use right angle headers, it doesn't really mess up the mounting and aesthetics (a term that doesn't really apply to my own home-etched boards) too much.
Trick 4: put the pads for the headers on the edge of the board, and use straight headers for a horizontal mount, or right-angle (RA) headers for a vertical mount. (bonus: no hole drilling required!)
The easiest way to do it, though, is to use SMT headers, like KE7GKP mentions. They take up more board real estate, but you don't have to drill holes which makes the PCB fabrication a [u]lot[/u] easier, IMO.
In a pinch, RA headers can be used as SMT headers. They need extra room, or trimming, though.