You can put lights on your patio umbrella in various ways.
With the aid of some mini clips, you can string them around the outside edge. Doing it this way will give you light both underneath and around the perimeter of the umbrella.
Wind them around the umbrella pole up to the center top. This will give you more light underneath and light a table or area underneath.
As long as your light string is long enough, you can run the light string up and down the spokes. This spreads the light more evenly for ambient lighting.