Go to the “free agent report” screen (under the GM/Contracts menus), and run a report of the Major League players on your team who are set to become free agents next season.
When the player names pop up, there should be a “negotiate” option on the right hand side. Click that; and it’ll take you to the contract negotiation screen.
You can only extend contracts if you’re in the last year of the contract, so if you have guys who won’t be free agents next year, you’ll have to wait. Most players will re-sign, with the exception of people who were taken to arbitration in their last arbitration year (they get annoyed that you didn’t sign them long term before the season) or guys who are likely to become Type A free agents. Most of them will want to test the market, though that depends on their patience rating.
By the way - if you forget to extend them this year, not a huge deal. Most (not all) will be willing to re-sign next year, and the second day of the season is set aside for you to re-sign players you want to keep. Sometimes it’s best to wait until after the season rolls over, as older players usually decline in ratings, and you may want to see how much the decline will be before you shell out the money.