Let me give you a quick rundown on getting better at pretty much everything in the game. You'll want to track down some trainers first, they're marked on your map and each one specializes in different skills. Training isn't free though and prices go up as you advance, starting around 100 Groschen for basics up to 5000 for the master stuff. When it comes to combat specifically, make sure to get those special moves like Master Strikes from the weapon trainers, really makes a difference.

Books are another solid way to learn, but you'll need certain skill levels to understand the advanced ones. The Scholarship skill makes reading faster and helps you learn more, so maybe interesting to invest in that early. There's usually four volumes for each subject and you can find them at scribes or through certain quests.

For hands-on experience, nothing beats actually doing the stuff you're trying to learn. The arena's great for combat practice, alchemy skills come from brewing lots of potions (Marigold ones are perfect for this), and if you want to get better at crafting just make a bunch of Broad Axes. As you level up skills, you'll get perk points which can make learning even faster, especially if you put them into Scholarship.

Good to know that mixing different learning methods usually works best - get the basics from a trainer, practice what you've learned, then maybe crack open some books to really master it. Combat skills are probably worth focusing on first, then think about Scholarship once you've got some decent equipment and want to speed up your learning.