I'm not an expert, but there are a few bullet points I'm aware of:
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Any strong alcohol has to be purchased at a state run store. 5% ABV beer can be found in grocery stores, but any hard liquor or wine or stronger beer goes through the state. Even restaurants, so it ends up being more expensive with the extra layer of profits. This was (basically) how it worked when/where I grew up in Washington (since changed), so it's not totally up to date with most places, but it's also not too far removed from being pretty normal.
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No ordering alcohol at a restaurant unless you also order food. Not sure what other states do. Maybe pretty normal, maybe not? Bars are fine, but the licensing is different and more limited. There were rules about bar areas in restaurants having to be more 'hidden' from the main dining area, but I think that's a thing of the past. And even older restaurants that haven't remodeled in the last decade+ still have drinks available. It was always a minor, performative hurdle.
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(edited in) The DUI limit in Utah is .05, which is lower than most states' .08. Whatever you think of alcohol, don't drink and drive.
For me, who just gets a few 6-packs per month to drink at home, I don't know all the other ins and outs. It's always a little funny to hear outside people tell me how archaic the rules are. Maybe someone who spends every weekend at a nightclub is right, and it's impossible to get a decent drink out on the town, but I don't do that, so it's not really a big deal.