Hi Dianne, welcome to DiscussCooking. Here is a basic, traditional carrot cake. My favorite way to serve this is as a double layer cake. If you do a double layer you will have to make more icing.
Cake
2 cups flour
2 cups sugar
2 teasp. baking soda
2 teasp. cinnamon
1 teasp. salt
3 cups grated carrots
4 eggs
1 teasp. vanilla extract
1 1/2 cup vegetable oil
Sift dry ingredients in a mixing bowl. Mix in grated carrots, vanilla, and eggs.
Beat, and add oil slowly. Pour into a buttered 8"x12" pan, or two 8" diameter round pans. Bake at 325° for 35-45 minutes or until the center is done.
Let cool completely before frosting.
Frosting
8 oz. cream cheese
1 stick butter
1 tablespoon vanilla extract
1 lb. powdered sugar
Beat cream cheese, adding butter and vanilla. Add powdered sugar a little at a time (like 1/4 box at a time) while beating. Frost cake.
You can add nuts to your cake as an option (walnuts or pecans) or add chopped nuts to the middle layer, or top with chopped nuts. (personally, I just want to taste that cream cheese icing!!!)