Warm air rises due to the fact it is less dense than cold air. This comes from the kinetic theory of gasses. Warmer air by definition has more kinetic energy per molecule. This frenetic bouncing around means the molecules, on average, occupy more space over a period of time. Put a bunch of these molecules in a group and the tendency is for them to spread out more, lowering the density.
The wind blows due to differences in temperature and pressure. By the ideal gas law PV=nRT, the higher temperature equates to a higher pressure. Since pressures being higher in one area will exert net forces on areas of lower pressure, the air will move toward the areas of lower pressure. This is experienced as wind on the earth's surface.
