The simplest approach is from Chisinau. Marshrutka minibuses run frequently from the Gară Centrală in the Moldovan capital; the trip takes about an hour and a half and costs a few euros. Drivers stop briefly at the Transnistrian checkpoint, where you fill in a short migration card; foreign passport holders are usually waved through with little discussion. Keep the slip of paper safe — you need it on the way out.
The other approach is from Tiraspol, only ten minutes by marshrutka or trolleybus across the road bridge over the Dniester. Many travellers combine the two in a single day trip from Chisinau: Tiraspol in the morning, Bender (Tighina) and the fortress in the afternoon. The international train from Chisinau to Odessa also passes through, but the timing rarely suits a sightseeing visit.