I use a Gillette cartridge razor for dick, balls, and ass, and just trim it all in the shower once a week.
>Dick & above
I find that going with the grain on the first pass, and then across the grain (not against) on the second pass, feels best. This way I don't get ingrown hairs, and within 2 days I have a softish stubble rather than one that's coarse and uncomfortable. On the shaft I do one pass against the grain down to the base of the dick. This can result in a slightly sharp stubble for the first few days, and if you jerk off for like 12 hours straight like me then it can leave a bit of a rash.
>Balls
Definitely do this in a warm shower, because you want your ball sack to be relaxed so that you can spread it into a flat surface. I lather them up real good, and then do one pass against the grain in a downward motion from the top of the shaft all the way down to where the balls meet the perineum/undercarriage. Don't go any further against the grain or you'll get the worst fucking itch ever.
Use a good quality razor, something like a Gillette fusion and not a cheap store brand razor. You won't cut your balls off so don't worry. I used to trim my pubes with a pair of scissors and I actually cut my ball sack with them one time, so I'm very careful now. With a good quality cartridge razor it's just not even a concern.
Try to spread the sack so that you're shaving on a flat surface, it'll help ensure that you don't miss any pubes.
>Undercarriage
Do a slav squat, and reapply shaving cream. Carefully (very slowly) make short strokes along the undercarriage with the grain (start at your ass cheeks and shave towards your balls), and then a second pass kind of off to the sides towards your legs. Don't go against the grain - this is the worst spot to get ingrown hairs and the regrowth itself is just pain and suffering.
The easiest part to cut here is going to be that little ridge of skin on the perineum called the perineal raphe, so try not to shave directly across it. i.e. don't center the blade on the ridge itself.
>Ass/asshole
Squat down again, lather up and carefully place the head of the razor against the inside of your asscheeks so that the blades are against the skin, and so that the tip of the razor (non-bladed part) is against your asshole. It helps if you place your finger on the back of the razor, as this way you can feel where you're placing it. Gently make small strokes leading outward, directly away from your asshole. Don't try to shave your asshole itself; you don't want to risk cutting it.
And because I'm going through withdrawals and I'm not even sure if what I've just said is understandable, here's a summary:
Dick & Above - With the grain and across the grain.
Balls - Against the grain.
Undercarriage - With the grain. Go easy, not too fast.
Ass/asshole - No idea. Shave away from butthole though.
Go against the grain if you like it really short and aren't bothered by itchiness or ingrown hairs. With the above strategy, you'll be left with a very tidy stubble that isn't as rough as you'd expect.
Exfoliating helps with ingrown hairs, and small amounts of benzyl peroxide can be used above your dick (never on your dick, ass, or balls).
Quality razors are important. I'd probably recommend NOT using a straight or DE razor, unless you're an absolute master at shaving with one.