The two main ways to improve troops are by leveling them and ascending them, both found by selecting the troop in question and going to the crafting area.
Leveling a troop is the easiest. By spending souls, a troop can be leveled as high as 20, depending on its rarity. The soul cost increases the higher the troop's base rarity is, as well as for subsequent levels. Leveling a troop gives it increased stats/skills (attack, life, armor, and magic).
|Current Rarity||Maximum Level|
Ascending a troop is different. Ascension causes a troop's rarity level to increase: for example, a Goblin - Common rarity - being ascended one level becomes a Rare. Ascending a troop requires extra copies of that troop, and further ascensions need more copies; a Common can be ascended all the way to Mythic level, but requires significantly more copies to do so. Ascension gives increased stats/skills similar to leveling, but additionally allows troops to be leveled higher due to their rarity increasing.
Troops can also be improved by unlocking their traits, discussed in this article: What Are Troop Traits And How Do I Get Them?.