In Witcher III your level determines a lot of your success in battle, but so does the amount of ability points you have farmed. Abilities increase your various active combat roles and alchemy, while your level increases your various statistics. 

Leveling Up - The Basics 

Like any RPG, you gain experience to level and when enough is reached, you'll level up. You gain experience from a variety of actions, from conversations (and using signs), to killing enemies (more XP if they're higher level than you, less XP if they're lower), and primarily from quests. The vast portion of XP you'll receive in the game will come from questing, so to that end there isn't any leveling secrets. Playing the game will increase your level. 

There are maximum of 70 levels. When you level, your statistics will increase and you'll gain one ability point. This means you'll get 69 ability points from leveling up, but that isn't the only source of ability points for Geralt to find.  

Ability Points 

Ability points (AP) come from leveling or Places of Power. There are 16 Places of Power throughout the map and you can get to the large portion of them rather early from exploring. Places of Power buff one of your signs for about half an hour and grant one ability point the first time you pull from them. You will never have enough ability points to max out every tree, but, as you level you'll gain more and more power (and you can only equip so many anyway). 

Once you purchase an ability, you can slot it on the ability screen. You can have 12 abilities active at any time. The slots are locked early in the game, but around level 30 you'll have all of them unlocked. You can also have 4 mutagens active at any time. 

Ability Respec 

You can respec your ability points by quaffing a Potion of Clerance, as shown in the in-game hints, available from various vendors. 

Mutagens 

Mutagens are dropped from enemies and at the end of the first prologue you'll get your first. If they match the color (effectively the type) of active ability slotted in the three slots beside it, then you'll receive a boost to that mutagen. 

My suggestion is to just load up on red mutagens in each slot with red active abilities (red - combat, green - vitality, blue - signs). 

Statistics 

The only statistic to worry with is vitality (increases health), which is increased through leveling and abilities and stamina, which increases your endurance. Armor decreases damage taken and DPS is determined by sword.

Ability Trees 

There are three ability trees and a fourth general tree (which I find to be powerful early on with its active abilities). 

Combat Branch: Increased Adrenline Gain by 1% per point spent. 

Sign Branch: Increases stamina regeneration by 1% per point spent. 

Alchemy Branch: Increases potion duration by 5% per point spent. 

General Branch: All active abilities and no benefit putting points into it. 

That about covers ability points and statistics in Witcher III. Happy monster hunting!