The occupier of property normally has to pay the council tax. However the owner has to pay if the occupancy is only temporary (e.g. 'holiday lets') or the property is classified as a 'house in multiple occupation' (HMO). The definition of an HMO is vague; see here:
http://www.landlordzone.co.uk/HMOs1.htm
(There are also a few other situations where the owner has to pay the Council Tax but they're unlikely to be relevant to you. For example, the owner is liable if all of the occupants of the house are under 18, if the house is occupied solely by asylum seekers or if the property is classified as a care home, hospital, hostel or women's refuge).
Pifalls?
Tenant who wreck the place and then disappear. Tenants who don't pay their rent and who prove difficult to evict. Periods without any tenant (and hence no income from the property). Failing to ensure that all of the relevant regulations are complied with (e.g. annual gas safety inspections). etc, etc!
Chris