Poti is a port city in Samegrelo.
[Poti] is a port city, meaning that there are several ferries arriving here from across the Black Sea. UKRFerry  offers a service from Varna via Ilyichevsk just outside Odessa. Departures are 1-2 times a week, prices range between €140-€320 depending on class. Ferries from Sochi are daily execpt Sunday, however this route may still be closed for nationals from non GIS-countries (ex Soviet republics) due to political conflicts between Russia and Georgia. A single journey costs 3,000 RUB. The service from Burgas via Novorossiysk with Intershipping  is currently suspended.
The airport in Poti has been closed since the collapse of the Soviet Union, however the government is planning to resume service by 2012. As of now Batumi International Airport  is the closest one, with flights from Baku, Istanbul, Kiev, Moscow and Tel Aviv amongst others. However, the number one gateway to Georgia is still via Tbilisi, not too far away.
European road E70, which starts in Spain, has its endpoint here. From Tbilisi, take the M27 road westwards and then turn off to A305 just outside the city of Senaki. A305 continues further to Batumi, so travel from there is straightforward.
Buses are plentiful from nearby Batumi, journey time is just about one hour.