Here are some general tips which might help you win the game more frequently. These assume you have fully unlocked all game mechanics and play to win (as opposed to, e.g. completing a specific challenge or trying to force a specific build).

1. Find A build, not THE build. To win, you must gain extremely powerful item/card synergy and focus on it. However, do not try to pick a build beforehand and force it. Although that could work, victory chances will be much greater if you just watch for whatever potentially powerful cards/items you will encounter, and adapt your build to those. After learning basic game mechanics, first 10-12 game stages are pretty easy, so you have time to pick a variety of cards and items with good potential. At stages 12-15 you have to make a decision, concentrate on chosen  build, maybe remove unneeded cards and hard-roll for missing cards/items to complete the build.
2. Choose next encounter carefully. With experience, you will learn to pick terrains with high chance of enemies vulnerable to your current hero, and not the other way around. For example, in the late game you might consider avoiding Cemetery when you have now way to prevent fear. On the other hand, if you have Helm of Courage, you may prefer Cemetery, since you are immune to the main threat there.
3. Hoard rerolls. Instead of rolling once or twice every stage, it is sometimes better to wait for favorable reward improvements (like additional cards/items, higher chances for upgraded/rare cards,  banishing effects like Porcelain Dove) and then spend rerolls with higher efficiency. This is especially true for cards, since adding marginally-useful  cards to the deck is more detrimental in short term than picking not-ideal item.
4. Pick cards speculatively and stash them until you find the rest of the combo. Some of the most powerful builds require 2 or even 3 pieces which are rather useless on their own. Stash provides room to collect those without jeopardizing your short-term power. In particular, do not be afraid to add 1 or 2 'off-color' cards even when you do not yet have a way to replenish resources in their cost.
5. Utilize quests to the maximum. Since quests are optional, the early game is much easier if you never accept them. However, quests are essential for smoothing out randomness and giving the player reliable path to victory. Remember that next quest offerings are influenced by the hero's current state. For example, picking 'ritual' card gives high chance to encounter a quest with 'Ritual Circle' card reward, which may be hard to find otherwise.
6. Look  for rare items / quests. Rare items are quite powerful, but the quests for them are hard and may be fatal if your hero is not prepared. Ideally you should familiarize yourself with those quests to be able to determine whether you are strong enough to take the quest when offered.
7. Be stingy with upgrades. Upgrades offer a guaranteed way to increase your power, which makes them tempting to do instead of rerolling rewards. However, many early-game cards provide comparatively small power increases when upgraded, so it may be better to save upgrades for the late game. With the exception of some permanent buffs which can increase your stats cumulatively if upgraded early, you should upgrade only when you power is otherwise insufficient to win the next stage. Vice versa, in the final 2-3 stages, it is usually beneficial to dump all your money into upgrades since your build should be already completed anyway.
8. Stash the cards before removing them. Since stashing is free, you can effectively remove up to 3 cards from your deck temporarily without spending gold. You can also use stash for rarely needed cards -- the most popular example is to stash healing cards for a hero with good defence, and only unstash them when the hero actually loses life.
9. Get rich quick. Look for gold-gaining items, quests and encounters in the early part of the game (approximately stages 2-8). Although it is possible to win the game without ever spending a coin, having enough money for multiple rerolls and upgrades is significantly more reliable.
10. Learn to break the game. Many items/cards have outright game-breaking strength which is not obvious from the first glance. Learning to recognize those and even find new ones not anticipated by developer is both a strong element of winning strategy and a lot of fun. Just as a random example, I know of at least 3 different ways (each with several variations) to gain infinite gold, and it is very possible that there is more.
11. Ignore all of the above. And have fun in whatever way you like :)

If you have your own ideas and strategies, please post them here or on our discord.

In recent versions, additional important strategy aspect is to plan card affinity.

Here are few points not (yet?) documented in-game:

1. Affinity between cards does not scale with number of similar effects or costs in the deck (e.g. if you have at least one card with “Melee” effect, gaining more cards with that effect does not further increase affinity).

2. Affinity is multiplicative between different “sources”, so for example if you have both St-cost cards and fire cards in deck, affinity of Pyre will be significantly higher than if only one of these conditions is met.

3. Items which directly name cards, such as Elephant Figurine, give strong affinity to those specific cards.

4. Affinity works regardless of stashing, so if you want to find specific off-color card, it may be useful to first pick any card with same cost just to stash it and increase chances of finding the original target.

Card banishment is another powerful method to narrow down the pool of card rewards.

1. All ban effects are ‘dynamic’, and can be undone by using Black Box, gaining resources in case of Anchor, or rearranging altar items in case of Altar of Missing God.

2. Similarly, banning card rewards does not affect existing cards in deck, but some related quests help to remove such cards without paying removal cost.

3. For high-level play, it is good idea in general to familiarize yourself with quest prerequisites. In particular, picking off-color altar items is now probably the most reliable way towards card banishment, since they not only enable Altar of Missing God, but are also prerequisites for corresponding quest, similar to ritual cards vs Ritual Circle.