First let me say that I am no expert fly fisherman..
Do you know the weight the rod is rated for (line weight, should be marked near the brand of the rod) as well as the reel, and what line weight is on the reel? That could be an issue. If a rod is rated for #6 WF line and you're using say #3 WF line it could be the rod is too stiff for the lighter weight. As apposed to bait cast type of fishing, fly fishing relies on the weight of the line to cast the fly, where as in bait cast, the weight of the lure pulls the line long in the cast.
As for technique, try not to flex your wrist while making the casting motion. Choose a position of comfort for you in the grip .. like thumb along the top in line with the rod, and pointer finger curled under.. keeping your wrist from flexing will help the rod flex as its intended to do in the cast. If your rod is a slow or moderate action rod your casting motion will need to be at a slower pace. If it's a fast action, then a faster pace. More often, todays graphite rods are in the faster category. Usually a slow action is a traditional bamboo rod. But, some companies make moderate speed rods too, but they are usually a pricier rod.
You can do a little research on the net to see what reel you have and what line it's rated for. Post on here and if I'm familiar with the reel I may know.. but often you can find the info. As for the line, unless you put it on yourself, you probably wont be able to tell what it is.