Carbon has a total of six electrons. Two electrons are s-type in the first energy level. The next two are s-type in the second energy level, while the final two are p-type in the second energy level. However, carbon has the ability to combine or hybridize the electrons on the second energy level to form what are called sp^3 hybrids.
Because of this hybridization, carbon can form four covalent bonds with other elements. The simplest carbon compound with four single bonds is methane, CH4 which is your compound.
To do a Lewis diagram involving carbon, first write down the carbon atom with one dot at four equal points around the C, showing the four bonding electrons. It is convenient to write the dots at 12:00 o'clock, 3:00 o'clock, 6:00 o'clock, and 9:00 o'clock.
Next put one hydrogen atom (H) with a single dot, next to each of the dots around the carbon atom. When you are done you should have four H atoms equally spaced around the central C, with two dots (bonding electrons) between the C and each of the H's. And your Lewis diagram is complete.