If you're going to get anywhere in Kingdom Come: Deliverance you're going to need to increase your skills, and luckily, all it takes is perseverance.
Just Do It
In Kingdom Come: Deliverance, you increase your skill levels by actually doing things. If you want to improve your swordsmanship, for example, you need to go out and engage in combat with a sword. Chances are you'll also improve your strength while you're at it. Want to improve your alchemy stat? You'll need to regularly concoct potions. Even reading is a skill that has to be learned and developed over time.
It's wise then, to engage in activities that develop the skills you want to develop. No matter how you're playing, at some point you're going to have to get involved in close combat, so take some time out once in a while to improve your combat skills.
Grab a bow and some arrows and head to a forest to hunt some game, or take your sword and shield and find some bandits. Ride your horse as much as possible, and don't be afraid to talk to all the interesting people you find on your adventure. It all works towards raising your main character level, and as you go you'll unlock perk points which can be used to further tweak the development of your character.
Make Use of Trainers
There are easier, and quicker ways to improve your skills, however. Trainers can be found across the land of Bohemia, and by giving them some coin they'll happily help you improve your skills. For combat, you can also spar with certain individuals which will allow you to safely develop your skills - like Captain Bernard who you can often find just outside of Rattay.
Complete Side Quests
Sometimes you may even find that completing quests improves certain skills, thanks to the quest-givers imparting their knowledge upon you. The gist of improving your skills in Kingdom Come: Deliverance then is to simply go out and explore the world, engaging in activities in the way you want to play. That way, you'll steadily improve the skills that you use frequently, and those that you don't you can improve by the use of trainers when you're relatively rich.
Kingdom Come: Deliverance's Bohemia is as beautiful as it is vast, so spending time in it really doesn't feel like a chore as you take Henry from being the son of a blacksmith to a famous, or infamous, warrior one step at a time.