The old town is small enough that walking is by far the easiest way to see Leiden. The longest walk you are likely to take is from the central station to the Hortus Botanicus at the far southern edge — about 25 minutes.
A bike makes life easier if you want to combine the centre with Naturalis or the medical centre on the outskirts. Cycle hire is available at the station and at several shops near the centre. Buses run from the station to the southern suburbs but are rarely needed for visitors.