Take marszrutka #26, #95, #99 or any other going to МОЛОДЕЖНОЕ from the central train station. Get off shortly after you see a huge bridge crossing the street (it is the intersection with the bypass around the city) and hitchhike straight on.
You can take the same marszrutkas 26, 95, 99, but just follow the bridge to the west for a few hundred meters. After turn right and find a nice spot for cars to stop. Or head towards the airport. Trolley-bus 8, 9 or bus 98, 115 (from Moskoltso), get off at Aeroflotskoye, walk about 300 metres and hitch from there.
Marshrutka 48 Gorbolnitsa - Khoshkeldy (Хошкельды (мнемоника: кошки+льды)), get off at the final stop Khoshkeldy, walk 200 m further to find a crossed Simferopol city sign. You can either hitch from here or go 1 km further up the hill past the gas station to a bus stop on a turn.
From the train station, take the trolley-bus Simferopol - Yalta. As of Nov. 2011, it costs about 13 UAH (1.6 USD), but provides an amazing experience and in 2.5 hours will get you to Yalta, Nikita Botanical Gardens being a few stops before the resort.