Cut your nails short. Fans of long nails may want to skip this step, but if you've managed to get dirt and grease all over your nails it's going to be a whole lot easier for you to get those nails clean if you cut them first. Most of the dirt will come off along with the nail tip, so you've just taken care of half the work already.
Use a strong hand soap to wash your hands, focusing on your nails. Massage the soap over the front of your nails and on the exposed underside of your nails too, if you can. You can even use a mild detergent, like dish soap, especially one formulated to remove grease. This isn't the best thing for your hands if you do it all the time, but is going to help clean off stubborn dirt and extra stubborn grease so it works for now.
Dry your hands and use the tip of a nail file to scrape the soil from your nails and get rid of any leftover dirt. There may be some embedded right down at the base of your nail that didn't come off during washing, but you can pick out that gunk with your trusty nail file, no problem.
Move a nail scrubber around over the top and sides of your nails. A nail scrubber is like a hard sponge, or sometimes a soft brush, so it scrapes off any dirt and grime on your nails. Scrub until your nails are totally clean. There should only be a bit of dirt if any left now, and don't scrub too hard -- overzealous scrubbing can take your skin off.
Rinse your nails to get rid of any leftover dirt and pat your hands dry. Now just try to keep your hands out of the dirt and grease -- at least until your next weekend project.
You can clean your fingernails in the shower too. You'll probably want to avoid cleaning them in the bath if they're covered in dirt and grease, so you're not left feeling like you're sitting in a deep fryer.
If you use dish detergent to clean your hands, and even just after all this scrubbing and washing to get your nails clean, it helps to moisturize your hands and nails.