I have a funky floral pattern in mind so I have created the individual elements and brought them into Illustrator. You can scan your own art and redraw it in Illustrator or use LiveTrace. Use whatever methods you are most comfortable with to create your elements. The only requirement is that your elements are vectors.
Select the Rectangle from the toolbar and double click to see the size dialog box. Use a whole number size (so the square fits in the grid) such as 30cm. Select View > Snap to Grid and align the background square to the grid. Drag guides to all four sides and allow them to snap to the grid.
Decide on a colour palette. Take inspiration from the season, colours around you, and colours you love. Try out a different palette from what you would normally use. Many surface-design clients have restrictions on the maximum number of colours that can be used, and depending on what surface the pattern will be printed on, they might already have a background colour in mind.
Make sure to take all of this into account, but don’t ever feel limited by restrictions. The challenge of surface design (and any creative work for that matter) is to work within restrictions in creative ways and make the project look great in the end. However, since this is for fun and we’re going for looks with this pattern, I will be working with 12 colours plus black and white. Start colouring your elements.