Bed slats are one of those items that seem to disappear every time you move. The bed will not be as comfortable with missing slats; it will most likely have soft spots in those areas. A box spring can also be damaged if it is used without all the slats underneath for support. Fortunately, there are a few different ways to purchase new slats.
Measure the size of slats that you will need. If you have one of the original slats left, measure the slat in all three dimensions. If not, measure the inside distance between the bed frame from one side to the other. Also measure the depth of the slat you should buy so that it fits flush with the top of the bed frame. In almost all cases, what is known as a "1-by" piece of lumber is what slats are made from. This is a reference to lumber that is 1 inch in depth, although in practice it is closer to 3/4 inch.
Call local furniture or mattress stores and ask if they sell bed slats. If so, you can have the slats in hand with just a quick trip down to pick them up.
Shop online for bed slats. They are available in many different types of wood, with cloth straps that will keep them from sliding around, and in different sizes. Keep in mind that these are usually more expensive than simple slats found locally, and you will have to pay shipping charges.
Take your measurements for the slats and go to a Lowe's, Home Depot, or other store that sells lumber. Inexpensive "1-by" lumber is available in many different lengths and widths at these places. You can save money this way and have your slats in hand quickly.