Well, there are a few abrasive, high grit pastes available. Diamond (0.5 and, I believe, 0.25 micron) sprays are popular, some people use ferric oxide - I believe those, along with CrOx are the main ones.
With the strop, a piece of leather lace or a shoelace or bit of string makes things very easy in terms of attachment to various things around the bathroom area such as door knobs or towel rails etc.
In terms of conditioning the leather, there's a tonne of leather conditioning creams and oils out there. But it really depends on the condition of the strop - if it seems supple and in good condition (and, as it has never been used I suspect it's probably OK), then just rubbing it with your palm before each stropping session will impart enough oil to keep it nice and conditioned. If it seems hard, then a good quality leather conditioner will help (I use a leather "cream" I picked up for good quality handbags - not my handbags, just handbags in general :))
James.