Fuente de Piedra itself has a small railway station, so it may be possible to go all the way by train from Málaga. See http://www.webmalaga.com/turismo/transportes/trenes/ficha.asp?cod=350&mun=29055 - I would suggest you e-mail them from the link on the page to find out times etc.
As others have said, going by bus all the way is another option and the bus station is very close to the railway station. However it would be useful to find out beforehand which bus companies go there. Each company has its own ticket office and sometimes it is not clear which company goes where, and therefore could result in a lot of queuing.
For time of buses from Antequera to Fuente de Piedra see: http://www.elsoldeantequera.com/autobuses/201-fuente-de-piedra.html
When we travel, Sue and I like to be independent to do our own thing and it usually involves getting off the beaten track to see places such as Torcal Nature Park. As a result, we almost always hire a car if it makes any sense at all given the circumstances of where we are visiting. In this case, because Sue's sister was joining us from England for eight days of our trip, I had to go one size larger than normal to accommodate three suitcases. It turned out to be a diesel Ford Focus station wagon with a 5-speed manual transmission. There was enough space in the rear for the suitcases plus a few other odds and ends as well as a flap that covered-up everything from prying eyes.
We hired it from Red Ribbon Car Hire Spain but picked it up from the Goldcar desk four days earlier away up the Mediterranean coast at the Alicante airport - at a daily rate of 18.26 Euros. However, when all the extras like insurance and diesel surcharge were added in, the total for 18 days came to 617 Euros.
Everywhere we went in Spain, we found the roads to be in excellent condition - even on small secondary roads in the Sierra Nevadas (like the one to Torcal) or along some 'off-the-beaten path' coastal roads. It did not give us any mechanical problems during the 3240-km (~2000 miles) we drove it and was just great in allowing us to reach the many smaller destinations on our trip. This photo was actually taken eight days later on a small Atlantic Ocean coastal road near Tarifa, Europe's southern-most point of land. The drive up to the peak of El Torcal was quite an interesting one on a switchback road with great views over the valley below - not for the faint of heart in some cases!
Antequera has a train station which is connected directly to Almeria, Granada and Sevilla. To get or go to other places by train you will have to change. For example to go from Cadiz I change at Dos Hermanas.
Antequera is and hour and a half from sevilla and another hour and a half from Granada by train.
The journey from malaga to Antequera has to be made by bus, which, we in the UK, would actually call a coach. Allow at least 15 minutes to walk from the railway station in Malaga, to the bus station. Sometimes crossing the busy roads can be a nightmare.
The bus company, CASADO, is located at window 21, and they probably won't speak English, but that is not a problem. The destinations and prices are shown on boards either side of the ticket office window.
The single fare to Antequera is (Mar 2003) 3.61 Euros. You will need to purchase your return (single) ticket at the other end!
I could never remember how to pronounce 'Antequera', so I used to tell myself we were visiting my 'Auntie Vera', hahaha!
There is a great train service between Fuengirola and Malaga, which stops at every local town, including Torremolinos. We decided to travel to Malaga by train, then catch the bus. The single train fare is only 1.65 Euros.
Trains run half-hourly, so not long to wait if you miss one.