For the absolute fastest and best results (and one of the messiest procedures (don't wear anything you don't want grease and dirt stains on)) Also, rubber gloves and eye protection are recommended
> Procure the PVC pipe in the method described above (the bigger diameter the better for speed and efficiency's sake)
> Soak/dunk the slides in mineral spirits instead of a water-based degreaser
> Keeping a bowl/small bucket of mineral spirits at the ready, brush the (now wet) slides with a stiff nylon brush and watch all dirt and grime completely wash away
> Rinse and repeat with mineral spirits 'til your heart's content
> Blast out remaining grease from nooks and crannies with compressed air
> Rinse and repeat with mineral spirits
> Put a fan on the (now clean) slides or let them sit in the sun until the mineral spirits evaporates off
> Relube with your choice of grease/oil/graphite/etc.
They'll be as close to new as anyone can get them without replacing parts
NOTE: Mineral spirits is a fantastic solvent/degreaser since it's (almost) endlessly reusable. All that filth that you dislodge during the process will settle to the bottom of the container (might have to wait overnight) and you can simply decant the mineral spirits into a bottle/jar for future use. If you want to clean it further, you can further filter it using a coffee filter (or paper towel) and a funnel.
Rags/towels soaked in mineral spirits should be laid or hung uncrumpled outside to dry before you throw them away.
***
DO NOT*** throw rags/towels/sawdust/etc soaked in mineral spirits in the trash can and walk away. Just like the warning labels state, rags soaked in that stuff WILL spontaneously combust and start a fire. It happens because mineral spirits releases heat as it evaporates and if there is not sufficient ventilation to permit the heat to escape, it will reach its flashpoint. For more on that topic, there are some videos of trash cans suddenly catching on fire to be seen on youtube.