Grinding noise when shifting

When I engage into first, and sometimes second, right when the car starts to "grab" (where I start moving right afterwards), I hear a grinding noise, until I move my feet a bit so that the shifting is different. Sorry if this doesn't make much sense, it's hard to explain. Anyone have an idea what's wrong? I'm guessing my clutch is starting to slip. If it is, any idea how much it would cost to get it fixed? I'd do it myself but I'm clueless as to how. Thanks.