Lorraine,
A high solids filler is the easiest way. Some water based fillers (I use Target) dry quickly and are easy to apply and sand off. Just apply, work it down into the grain by wiping across grain in different directions, then scrape diagonally across grain with a plastic wiper (credit card works well).
When dry, sand surface smooth (220) and check if it needs a second application. Don't be afraid of sanding ALL the filler off the surface leaving it only in the grain pockets.
But if you plan on staining your project, know that some fillers will inhibit the coloring a little bit. Stains, dyes and finishes sometimes don't darken the piece as well as if filler was not used. That's why they always say...."practice on a similar piece of wood first".
Good Luck