A typical start.
Endless mode cheese.
You gain experience through kills (and certain other sources), and with enough of it you level up, which most importantly gives you a skill and is needed to unlock two dice. The maximum level is 10, and it doesn't persist between scenario runs (dice upgrades you acquire in a scenario are also reset).
If you have a monster-capturing die side (consumed on use), or a capture/summon spell, you can put an enemy in one of your dice, which provides you with a special ability of theirs. The necromancer class is leaning towards keeping a number of allies at all times, with frequent sacrificing and replacing of them. Certain scenarios also have strategically-placed weak monsters early on that may provide you with an ability that counters some annoyances in later waves.
In theory you could fill your dice with 5 red "skip this side" symbols on each to always receive the same result on rolling them. Having a variety of attacks with different effects and getting to them via rerolls if you need a specific one tends to be more useful, though. Colored backgrounds are negative effects applied by certain enemies.
Timebender is a fudgemaster class that can gain a silly amount of rerolls. The black circular arrow on some sides here means that if you roll such a side but decide to reroll, you will still use it for free.
You can equip up to 4 artifacts for each scenario (the exact amount depends on the selected scenario), with effects ranging from minor benefits to make the beginning of the run easier (such as adding some symbols to starting dice), to adding new mechanics that affect your strategy for the run (e.g. witch's knife will make you focus on collecting as many cursing sides as you can, as they become infectious and will keep spreading their stackable effect to other enemies, another item will give you a new skill whenever you use up all the charges on one, or you can mix an artifact that guarantees a chest drop on overkill with one that increases your attack power with each opened chest)
The endless mode difficulty can be quite unpredictable because of you having to select for yourself one of randomized penalties after a number of completed waves, and some of those can be very punishing.
Classes aren't prevented from eventually gaining dice sides or skills belonging to other classes, but the chance of acquiring them is lower (e.g. the barbarian will get sword and axe attacks in the shop more frequently than the others, and the cleric will mostly get white- and blue-gem skills) and the starting dice/skill setup is different for each class.
Not killing a wave before before the turn limit for it runs out doesn't mean immediate loss (the remaining enemies deal a round of special damage to you, and you progress to the next wave), but you will lose on the benefits you get after defeating each wave, and it will likely prevent you from getting 5 stars for the run. Some scenarios have very forgiving turn limits (but the quicker you are, the better score you get), some may challenge you to beat a group of enemies (or a hard-to-damage one) with very little time for that, so in those each move counts (and skills that deal direct damage are doubly-useful).