My Gears Are not Shifting Well
If you can't get out of the lowest (easiest) gears then something is stopping the cable from releasing. There could be a number of reasons for this. The shifter on the handlebars might not be working properly, something may be caught on the cable and pulling it, the cable could be frayed and is snagging on something, or the rear dérailleur could be jammed.

So you should do some diagnostic tests: if you try to put it into highest (fastest) gear and the cable goes slack but the rear dérailleur doesn't move then it's not the shifter, so you can rule that out. If you undo the nut that holds on the cable to the dérailleur and the dérailleur moves, then it's the cable, and if it doesn't then it's the probably the dérailleur.