I assume you know how to disassemble your bearings for clearing. If
not, don't be shy to ask.
Anyway, you would need two substances to clean them. Both can be
bought at your skate shop or at a larger sports store. One is
"degreaser", that also goes under monikers of "solvent", "citric
solution" etc. It dissolves old remnants of lube, broken down
fractions of it, and washes away the dirt that gets into the bearings
from the outside world. You'd likely to see Kryptonics, Racetec, BSB
and other brands -- they all would do the job. The second agent is the
new lube itself. You can select from a range of oils, gels, and
creams, depending on desired speed/longevity ratio. Gels are slower
but last longer and keep dirt out somewhat better. Oils are faster but
break down sooner that gels, so you have to relube more often. There's
seemingly an infinite range of opinions on what's better for a
recreational run-of-the-mill skating.
It's worth mentioning that some skaters prefer to use ol' trusty WD-40
for both cleaning and lubing purposes, because it's cheaper and
"better". Some use gun oil, even, and I won't be surprised if someone
out there is using K-Gel brand commonly reserved as a lubricant for
anal sex. You see, there are many opinions :) . One thing for sure:
just don't use dish detergent and hot water, as someone recently
"advised" in this newsgroup. Steel doesn't take it well to water.
Good luck,
V.