Patan sits directly across the Bagmati River from Kathmandu, and getting between the two is straightforward. A taxi from Thamel takes about twenty minutes outside of rush hour, and about an hour in it. Microbuses run frequently from the Ratna Park bus stand in central Kathmandu to Lagankhel in southern Patan for a few rupees.
If you are arriving from outside the valley, you will land at Tribhuvan International Airport in Kathmandu. From there a prepaid taxi to Patan costs roughly the same as one to Thamel.