Look for a small circular metal insert in the housing near the head bearing, about a 1/4 inch across with what looks like a BB in the middle of it. It will be flush with the whatever it's in, not stuck out like a traditional grease fitting. It's a zirk (or zirt, depending on who you talk to) type grease fitting. They're popular in many machines. You'll need a grease needle (ones with a fatter, tapered needle, not the super thin needle ones) to fill them. The easiest place to get one is go into the automotive department at Walmart. They usually keep them on a wall/peg type display near the oil products. Screw that onto the end of your grease gun. They're $4.97 if I remember right.
There probably is grease in it already, but trust nothing that comes with a Ching-lish manual.
Believe it or not, the best thing I've found to keep your new toy from corroding, and still being enviro-friendly, wife (what is that smell) friendly, and a cheap skate

is vegetable oil or peanut oil. The only exposed, high pressure point on your lathe is the tool bit, and you're not worried about that. Use normal cutting fluid. We used peanut oil on saddle bearings (bronze, friction type) bearings in plastic manufacturing plants for years, and those shafts see a heck of a lot more wear factor in one day than your lathes gears, feed screws and bedways will see in a lifetime. It's also non toxic.