The skills screen is split into 3 main areas with the left hand side showing you the various skills you can unlock and select, the middle area displays the traditional tree slots whilst the right side is reserved for hints and your character stats.
To open the Ability screen simply go to the in-game menu and select Character. The tradeoff is that there's a limit on the maximum number of active skills, no matter how many you've already unlocked. The skill tree in the Witcher 3 is more dynamic compared to other games, allowing you to swap in skills depending on the challenge ahead.
From here you can unlock new Abilities and select a limited number to improve your characters overall rating in areas such as Combat, Alchemy, Signs etc. The Ability screen (or skill tree screen) is part of your characters development in the Witcher 3.