Most digital multimeters look like this:

1 = Display, 2 = Function switch, 3 = Transistor socket (optional), 4...6 = Test lead jacks

If your meter has a transistor socket, set the function switch to hFE and simply insert the transistor leads into the proper holes of the socket. To determine the type (NPN/PNP) and to locate the B, C and E leads, use the transistor's datasheet. The display will show the transistor's current gain (h_FE).

If your meter doesn't have a hFE test, you can at least test the BE and CB diodes using the diode test.