Baseball, football, basketball and hockey cards go through the same three routes as any other card: a local shop that handles grading submissions, a card show where a grading company or a dealer takes submissions, or sending the cards to the grading company yourself. Sports card shops are the most likely local option, because many of them already buy and sell graded cards and know what each company expects. Start with sports card shops or MLB baseball card shops, then check the grading and submission shops in your state for listings that state the service outright.
Prepare the cards before you go. Sleeve and top-load each one, write down the player, year, set and card number, and decide which cards are worth the fee by comparing recent sold prices for the raw card against realistic graded results, not only a perfect grade. Vintage cards need extra care; a shop that deals in vintage can tell you when a card is at risk of coming back as altered or trimmed. At a show, ask whether the table belongs to the grading company itself or to a dealer submitting on your behalf, because that changes who is responsible for the cards until they come back. Upcoming shows are on the card show calendar.