There is an old myth that if your pedals spin forever they are in great shape. The truth is, it means that the grease has 'dissolved', become liquefied, and most of it will be on the inside of the pedal body, leaving your bearings and bearing races exposed to quick wear.
With Shimano DX pedals, as with most pedals, the plastic caps are removable so you can remove the axle and bearings to re-pack them. You will though, undoubtedly, damage your end caps if there is even the slightest burring of alloy on the end of the pedal.
Anyway, to start with the re-pack, you will require a 15mm spanner, an 11mm socket and wrench, a pair of thin nosed pliers, and two small flat head screwdrivers. A wire brush is also handy to rub off any rust or debris on the axle thread ends.
First we are going to take the pedals, one at a time, and remove the end caps. I recommend doing the pedals one at a time so there is no chance of mixing the bodies and axles up, and the bearings from each pedal will go back from whence they came
Screw the cap anti clockwise using the thin nosed pliers. Once you have unscrewed the cap as far as it will come, gently prize the small screwdriver down the side and prize the cap upwards. There are slots around the cap on the underside which you will see, so make sure the screwdriver gets into one of those to minimise any damage.
Once you removed the cap, you will require the 13mm socket and wrench and the 15mm spanner. The securing nut on the end of the axle will undo anticlockwise (This is for both pedals).
Unscrew the locking nut, then remove the lock washer.
Unscrew the bearing nut by securing with the thin nosed pliers and twisting the axle with your other hand in a anticlockwise direction as you look at it.
Slide out the axle, remove all the bearings carefully. I like to place them in the cap so I know where they are and they can't roll anywhere. There should 22 of them.
Now clean the bearing races inside the body with a clean rag. For stubborn, dry grease, use some white spirit.
Clean the threaded end of the axle with the wire brush, taking care not to damage or 'remove' the weatherproof seals.
I like to use Teflon Grease, and Finish Line is a great product
With your flat edged screwdriver, take the grease and lay it on the bearing races at both ends. Drop 11 bearings onto the grease and use the screwdriver to 'push them home' onto the races in the grease and remove any excess. Wipe the inside carefully to also remove any excess.
Now place you axle carefully back into body and push it all the way through.
Firstly, screw on the bearing nut and replace the lock washer.
Screw on the locking nut until it just pinches the lock washer and tighten slightly with the 13mm socket. With your thin nosed pliers, hold the bearing nut and tighten the axle with the 15mm spanner in a clockwise direction as you look at it. This will tighten the bearing nut against the lock washer and locking nut. You may have to do this a couple of times to ensure you have the correct spin on your pedals.
If they are overtightened, you will force the bearings into the races heavily and will damage both. It they are too loose, the play in the axle will put pressure on the bearings and the races, thus also causing damage. Once you are happy with how the pedals spin, replace the caps, and voilà. Ready to roll for another couple of months
Any questions, just feel free to ask