I'm an experienced player, and i have noticed a lot of basic play mistakes are being made on the dominion steam app. i wanted to share a few things i see frequently, why they are bad, and some tips to help improve your win rate. I will keep examples focused on the early sets .

1 Skipping thinners

Trashing your starter coppers and estates is really important. Put simply, it lets you play your better cards more often. In almost every case, a player who focuses on thinning out their starting cards quickly will easily beat a player who doesn't. Therefore, trashing should be the highest priority and should normally be your opening purchase if possible.

There are two kinds of trashers in the game. "Thinners" remove cards from your deck and make your overall deck smaller (cards like chapel, moneylender, steward). "Trash-for-benefit" (remodel, trader, mine) typically will swap one card for another (although note that trader can thin coppers since you gain nothing from them). These don't actually reduce the total size of your deck, but you have improved it (probably). There are occasions where cards like remodel can be thinners - for example, if you have a 2c cantrip card like pawn or farrier in the kingdom, then you can remodel a copper into that cantrip, which effectively shrinks the size of your deck.

Steward is a very commonly skipped thinner. I often play games where I open Steward/Silver and my opponent skips the steward entirely. I can almost stop the game there and declare victory, because i know that the cumulative advantage that this steward will give me simply by trashing 2 cards at a time is going to win the game.

An additional note to the above: prioritise trashing over other actions or buys. This is so important. I very frequently see my opponent not using their opening trashers in the first few shuffles, which is almost the same as not buying the trasher at all. If you have a hand with steward, estate, 3 coppers, you should just suck it up and trash estate + copper and buy nothing. You will be much better off doing that than using the steward for +cards or +coin. An exception to this would be if you needed to hit 5c for another key trasher such as sentry, but 90%+ of the time, just trash and pass. Trash first, build later.

2 Opening Village

A second mistake which is extremely commonly seen is to buy a village (or equivalent) on the opening turns. Village is +1 card, +2 actions. You have nothing to do with the extra action, and the draw simply replaces itself. Therefore, buying a village on the opening turns does nothing to help your deck. The first few purchases are extremely important, because you need them to help your deck crawl out of the early game. Wasting a precious opening purchase on a village is a huge mistake, and it indicates a poor understanding of how to quickly build your deck. As mentioned above, your top priority should be a trasher. If there are no trashers, you can instead look at gainers (workshop - assuming there is an engine to build and villages available), draw (smithy, etc), attacks (militia, swindler) or other strong payload cards which will help you build your deck up.

3 Too many terminals

We are generally only able to play 1 terminal action per turn. A very frequent mistake is to open with 2x terminal cards (cards which don't give at least +1 action). This means they can often end up with a "collision" (drawing both terminal cards in the same hand, and only able to play one). This is especially bad when you open with a terminal draw card like smithy or moat, since you have a high chance of "drawing dead" (drawing into a terminal collision). There are some terminal cards which let you mitigate this (e.g. courtyard, gear), so those are more reasonable to open with.

Beyond the opening, i still frequently see players with just too many terminal cards in their deck. This can include strong cards like militia, witch, smithy - but if you have too many of them, and not enough ways to gain + action (villages etc), you will often be stuck with these terminal cards in your hand. This is called being "over-terminalled". This can be quite a big issue since you will not only miss out on the opportunity to play them, but they also "block" your draws - if you play smithy with your last action, you would rather draw a copper than a witch, for example. So the key is to balance having enough villages to play your terminal actions. A good rule of thumb is to match each terminal card after the first one with a village. So, first smithy is free, and thereafter each new smithy purchase should be followed by a village purchase. Even if you have a hand with 4 money, if it's time to buy a village, you should buy that village.

In kingdoms with no villages (no village/throne room/festivals), you need to accept that you will not be able to have many terminal actions. Generally 2 is all that your deck can sustain (if there is no trashing, then this can rise a bit over the course of the game). Kingdoms with no village are often dominated by "money" strategies - buy those 1-2 key terminal actions, and then focus on getting money and green cards. (tip 3.5: Don't try to build an engine when there isn't one available).

4 Lurker

I want to mention this card in particular because i see people overplaying it all the time and losing as a result. Lurker is a classic newbie trap card. It promises great things (non-terminal gainer for any price action, wow). In some kingdoms, it's powerful (with fortress, trail, hunting grounds, cultist). Even in a potion kingdom, or a kingdom with very expensive actions like king's court it can also be okay-ish. But it's almost never a good purchase in the opening because it is too easy to counter. If your opponent gets lurker, you can either ignore it, or you can buy one lurker in response - and pay attention to when your opponent is playing their lurkers and you can either "steal" their trashed cards, or simply force them to wait until they have 2x lurkers in hand, at which point they can gain any card. This sounds pretty reasonable until you realise that 2x silver would achieve the same thing most of the time. I have seen players frantically buying 5-6 lurkers in the early game, and then spending the next several turns either gaining a single 5c card, or passing. So, don't fall for the lurker trap - it's a bad card and you should generally avoid it!

Conclusion:

Dominion is a game of small edges, and prioritisation. Most of the above mistakes can be captured by a simple rule: prioritise your purchases correctly - trashing above all, followed by building your deck in a sensible fashion. There are many more beginner mistakes, but these are a few, and hopefully this is useful for those who are learning the game. Please feel free to ask about these tips and try to understand why they are here. Experienced players might want to chip in with their own observations.