Valence Bond Model of the Double Bond
At right is a 3-D version of the Lewis structure of the ethylene molecule.  You may rotate the molecule yourself by holding the mouse button down while dragging it around within the image frame.  Dark grey spheres represent C atoms and light grey (white) spheres represent hydrogen atoms.  Single bonds are represented as single sticks and double bonds as a pair of sticks.  To return to this view at any time click on the button below:

Each carbon atom is surrounded by three "groups" as specified in the VSEPR model for molecular shapes.  An atom surrounded by three groups will be sp² hybridized to get orbitals pointing in the correct directions to make bonds at 120 degrees from each other. Click the button below to show these hybrid orbitals on one C.
Single bonds (σ-bonds) are made by overlapping hybrid orbitals pointed along the bonds.  The σ-bond that is part of the double bond in ethylene is made by the overlapping sp² hybrids on the neighboring C atoms. Click on the button below to show the hybrid orbitals on the other C atom and the overlap forming the σ-bond.
The bonds to the H atoms are made by overlapping the remaining hybrid orbitals with the H 1s orbitals.  Click on the button below to add the H 1s orbitals.
This represents the σ-bonding framework of the ethylene molecule.

π-bonds are made by the side-on overlap of p orbitals on neighboring atoms.  To add the two p orbitals that are left over on the carbons from the formation of the sp² hybrid orbitals click on the button below.
The yellow orbitals are the p orbitals.

To show how the two p orbitals combine to make a π-bond click on the button below. The red surface indicates how the two yellow p orbitals overlap. To remove the p orbitals and leave the π-bond click on the button below. This model shows the double bond as the σ-type overlap of the sp² hybrid orbitals (in blue) plus the π-type overlap of the p orbitals (in red).  The electron density above and below the bond in the π-bond prevents the two ends of the molecule from rotating relative to each other about the C–C bond; thus maintaining the planar geometry of the molecule.

To show just the π-bond click on the button below.
You may look at any of these intermediate views again by clicking on the appropriate button.