Bus:
There's a regular bus # K-678 daily from Ozerki metro station in St. Petersburg (North). The bus departs Ozerki at 9am, 11am, 2.30pm, 4.30pm, 7.20pm, 9pm and takes about 1 hour 50 minutes to Korobitsyno (Krasnoye Ozero). The bus from Korobitsyno to Krasnoye Ozero departs at 6.30am, 7.20am, 11.40am, 1.40pm, 5.10pm, 7pm, 9.40pm and also takes about 1 h 50 minutes.
Train:
There are no trains directly to the resort, but you can take a local train (elektrichka) to Pervomaiskoe or Sosnovo (from Vyborsky station in St. Petersburg) and take a taxi or a local bus from there. However, if your Russian skills are not so good, it's better to take a bus from Ozerki metro.
Driving:
Exit St. Petersburg and take the road to Vyborg (Vyborgskoe Shosse towards the Finnish border). After the sign pointing to Zelenogorsk, you need to turn right and drive towards Pervomaiskoe. The road is bad, so be careful. Once you are in Pervomaiskoe and see a crossing, you need to turn left and then right -- towards Michurinskoe. The resort is after Korobitsyno village. For driving directions scheme, see the resort website at http://www.zoldol.spb.ru/index.php?area=address
Flying:
The planes to St. Petersburg arrive to Pulkovo airport, which is quite far from the resort. You will need to go across the city and drive towards Vyborg.