How can I extend window stools so I can add trim?

Cut pieces of wood the length you want and as deep as the 3/4" extension. Predrill holes so you can nail to the wall. Use some Liquid Nails or similar to glue to the wall and sill. Use a level to make sure they are straight with the rest of the sill. Use long finish nails to nail into the wall. Countersink the nails. Fill the nail holes and the gap between the old and new sill with wood putty.

what about just adding a piece of bullnose trim to extend it out then new full length bottom trim pieces under bullnose to make it look like it is all one piece, you'll need to use some wood putty to make bullnose trim piece look seamless,but after you sand it some and repaint should look fine. or if bullnose isn't wide enuf you'll need to cut a piece off of board used for stool/sill just so it matches.it won't be as strong as solid stool but you can get it too look like it's one piece.after you add side trim up window from stool/sill it should look fine

If you are not inclined to remove the stools, you could try covering them. It looks like you have enough height from the existing stool to the top of the bottom part of the window frame. Experiment with a piece of 3/4" stock like a 1x8. If a 3/4 " height is too high, try a thinner piece of stock. Cut it so it is a little deeper than the existing stool and as wide as you want on the sides. You can add trim around the front and sides, attached to the bottom of the new stool, to make it look like another layer of apron molding. Then add the side trim as William suggested. You might waste some money on wood, but you can determine if it is worth investing in such a solution for all the windows. I would bite the bullet and replace the stools. If you do, there is a good chance the aprons are nailed to them, so deconstruct carefully.

I just cut my sill even with the edge of the window then framed out the whole window.

The window casing should sit on the stools . The stool should be 1/2-3/4 passed the casing ! Might be easier to replace them !

It looks to me as though the bottom trim under the sill was the last piece added. I would carefully remove it to not damage the sill. You'll be replacing the bottom molding but they still sell that bottom profile molding at places like Home Depot - you can even get it primed!

Then, I would do as William suggested and extend the existing sill to the sides as far as you like. Put on your new vertical molding and finally re-cut/replace the bottom trim at a new, attractive width.