All skills are unlocked to their max level. 

While Shortz has answered your question, I made a picture here for you in case you are a visual person like myself.

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For my Arbiter here; basically you go into the tavern and select "Upgrade Skills" (green arrow) from the options. Since she is a legendary champ, you can select either Legend or Mythic books (yellow circle) to upgrade her skills. Her skills and their levels (blue circle) show at what level they are currently at.

Typically, the higher the book, the rarer it is to obtain. While you could use a Mythic book to upgrade her, about 99% of the community will tell you that's a bad idea. The more levels in a skill, usually the more DPS they produce. Either by adding more dmage/healing from the skill or by shortening the cool down on it and thus getting back to that skill quicker.

If you have a new account, it becomes a game of who do you upgrade their skills first. Often, you will get champs faster than you will get books. Even after 5 years playing the game now, I still have champs that are level 60 and I haven't upgraded their skills yet. Not to mention that I have probably 50-70 legend champs in my vault at level 50 with no books either.

If you're scared or not sure who you should book first, feel free to post your roster here and let people help coach you. Also, it's not uncommon to be upgrading a champ when suddenly you get a better champ and focus on them instead of the first one you were working on. Basically, I would recommend saving your books up before just spending them 1 at a time as soon as you get them. You might have a champ that's either 3.5 or 4 stars out of 5; only to get a 5 star champ that you suddenly wished you had books for.

That's my recommendation to you. Even after 5 years playing, I'm still not an expert. There are people around here that are better at strategy than I am.