I do this with my Tascam 246 (cassette 4 track), but I think the 388 is a little different in the way it syncs. Basically, you'd stripe a time code on track 8 of the 388 with a time code generator. On the four track, the code generator just connects via an audio cable to a sync input (RCA jack I think) on the machine, but I think the 388 has a different type of input for the sync (though I could be wrong). In the 388 manual, there's an illustration showing a sync box, and it looks as though it's just connected to RCA inputs, but it's hard to tell exactly what's going on. If that is the case, then you could probably use something like a JL Cooper PPS-1 (or 2 or 3), which can be had for around $50 or $60.
Anyway, then you connect a MIDI cable from your drum machine to the code generator, which allows the drum machine to chase the 388.
Instead of using an external drum machine, though, I'd recommend the plugin EZ Drummer 2. At $150 (I think), it's cheaper than most of the better drum machines out there, and it will blow them away in sound quality/flexibility. The sounds are 100% pro level without a doubt, and its interface is awesome too.