The Quarry missions are similar to the Trucking missions in that once all have been completed you'll unlock the Quarry as an asset that provides up to 2000 per day.
A timed mission that requires you to push seven rocks into their markers. Quite simple as long as you know your way around the quarry and get the hang of the vehicle controls. Push the rocks a bit so they gain momentum and pop off the ledges on their own.
A timed mission that's similar to the one above, but now you'll have to push the barrels into a specific location. The barrels go off when placed in the correct location, avoid the blast radius. The barrels will continue moving after you've given them some speed.
A timed chase using a dumper. The dumper truck is very forgiving off-road, and the easiest way to complete this mission is to drive up alongside the target truck and do a drive by until it's on fire. Or you could be a bit more creative than that if you so please.
Yet another timed mission, hop on the bike and head around the quarry (either way is okay). Then swap vehicle and drive carefully back to the main gate (if you crash/run into something you might drop a corpse which ends the mission). Head down into the quarry and back up towards the fire and dump your load in the general vicinity of the fire. Pressing reverse as you dump will keep the dumper truck stationary.
A timed mission, drive carefully to the desert airstrip. The dumper is pretty good off-road, you might want to head down the road towards the train crossing and ammu-nation. There, cross over to the larger road that leads to Las Venturas, once up the hill swap over to the desert road and then you're almost there. Skim past the car dealership next to the airstrip and go down the runway until you reach the waypoint. As long as you watch the traffic you'll be fine.
A timed mission, clear the railway tracks with a bulldozer. Head along the same route you took in the previous mission. Then head onto the railway tracks. The easiest (or at least the quickest) route to clear the tracks is to zigzag, that is approach a barrel at an oblique angle, push it a bit so it gains momentum and rolls off the tracks. Then continue to the next. As long as all barrels roll off and don't stop early needing correction you'll clear the lot with ample time left to go.
Then get off the tracks yourself, a scripted very fast moving train then spawns that is heading towards San Fierro along the track.
The final mission, timed but with plenty of time to go as long as you don't get stuck on a particular segment.
Get on the bike and head down into the center of the quarry. There push the bike and the corpse into the marker. It helps if you don't accelerate all the time, nudge them instead (otherwise you might loose control over them on the uneven terrain). Then get on the bike again to save time and drive up to the crane.
The crane controls may be a bit confusing at first, you control up-down and near-far from the crane column. The camera will follow the magnet, keep this in mind. It helps to observe the shadow on the ground when determining when to drop the bike and corpse onto the dumper. Once you've done this, drive carefully up to the entrance (careful as in don't collide with anything, you may do it at full speed and jump and such as long as you don't collide, this will cause the cargo to become loose until you stop completely); then cross the highway carefully and dump the contents into the water as you did back in mission 4.
After you're done, you've unlocked the asset and are told the time it took to complete all quarry missions (which you may wish to beat should you be inclined to do so).