There are two kinds of mantel clocks---pendulum and non-pendulum. Adjustments are made differently on each type. Setting the time however, is the same on each. Before adjusting the clock make sure that the pendulum is hung---if there is one--and that the clock is level. Generally you should wait a week after installation before making adjustments for timekeeping accuracy. The clock will settle down during this period. You also might need to make seasonal adjustments.
Set the time. Move the minute hand backwards (counter-clockwise) until the hour and the minute hand are at the correct time. Don't move the hour hand; it will move on its own as you adjust the minute hand. Some clocks might need to be adjusted by moving the minute hand clockwise. Many clocks let you bypass stopping at each hour and waiting for the chimes to strike, but for some you need to wait. Follow the instructions for your specific clock.
Wind the clock. The clock can have up to three winding key holes. Turn the key clockwise. For clocks with weights, raise the weights using the crank. If the clock does not have a pendulum, the clock will start on its own. If it has a pendulum, reach into the innards and grasp the pendulum. Move the pendulum to the left and let go; the clock will start.
Regulate the timekeeping. Pick a time of day that you will be able to check on the clock. You only need a couple of minutes, but it should be the same time each day for up to six days.
Write down the correct time, and double-check that the the minute hand on the mantel clock is correct.
The next day, come back to the clock at the same time, and compare the time shown on the clock with the correct time.
Adjust appropriately. On clocks with a pendulum, move the pendulum disk up to speed up the clock or down to slow it. Use the adjustment nut; turn it to the right to move the disk up and to the left to lower it. On clocks without a pendulum, just move the time adjustment lever. Pushing it toward the minus slows the clock, and pushing it toward the plus speeds the clock up.
Repeat for up to six days, until the clock is keeping correct time.