1. Go to the Otogar and ask to go to Birecik. Any bus to Urfa will get you there.
2. You'll get dropped off at the side of the road in Birecik, on the east bank of the Euphrates (you're in Mesopotamea now!). Walk down to the river and walk north (upstream) for about 600 - 800 m until you are adjacent to the castle. You'll find some minibuses waiting next to the river; ask for the one to Halfeti. If you go on google maps there a shopping bag symbol labled "sebzi hali" adjacent to where the minibuses wait (there are minibuses at a few locations along the river so be sure that you've walked far enough).
3. The minibus will drop you in Yeni (new) Halfeti. There may be a minibus waiting to go on to Eski (old) Halfeti from there.
4. Once in Eski Halfeti, there are lots of boats that take you out onto the lake and round Rummkale (the boat I was on didnt land though).
I've seen plenty of people say that they had no trouble getting toHalfeti, but I had a hell of a time getting there and back. Part of that was not knowing where to go in Birecik, but my methods of transport to and from Eski Halfeti were an old bloke who offered me a lift and a French tour bus! Its certainly doable as a day trip, but I'd suggest you leave early and be prepared for a bit of an adventure if things don't go smoothly. I'd also imagine that things might be a bit more difficult at this time of year than in summer.
Having said that, Birecik alone is worth a visit, and Halfeti is lovely. At worst, you might be able to pay the minibus extra to take you to Eski Halfeti and there are resteraunts down by the water who would be able to help you get back in a pinch.
Once again, lots of people seem to have few troubles getting there, but its better to be ready to improvise if you have to. If you're in Gaziantep already, you'll know how lovely people are in that area, but you should always be careful if you're a woman alone.