It's not a big deal, we were all beginners at one point. Long long ago...
ok to make it easy let's say you make a deposit of $20 and you get a 100% match deposit with a 20x wagering requirement. You're starting out with $40 - $20 of your own money and $20 of casino bonus money.
Depending on the casino and the software the wagering requirement (WR) can either apply ONLY to the bonus money, or they apply to your deposit PLUS the bonus.
If it applies ONLY to the bonus money then the WR is $20x20 = $400 and if it's the deposit AND bonus then it's $40x20 = $800
So that means that you have to make $400 (or $800) in bets before being eligible for a withdrawal. Every bet you make whether you win or lose goes toward satisfying the requirements. Usually slots play is 100% - that means if you bet one dollar, the whole dollar value is applied to WR. Other games may only count 75% or less to WR - so if you bet a dollar, only 75 cents of your bet is applied to WR.
*Please be sure to read terms and conditions when taking a bonus because some games are not allowed - if you play them there's a big chance that your winnings will be forfeit!! If you take a bonus, read the terms and if you're not sure, then check with support.
If you're going to take a bonus, I'd stick with places that make it really easy to understand. Most Microgaming casinos have something called the ClearPlay system - it shows your regular balance and your bonus balance when you hover your mouse over where your balance is. The bonus balance is transferred to your real balance in increments of $10 as WR are met. When your bonus balance is at 0 then you know your wagering is done.
A lot of RTG casinos have it built into the cashier also. Most RTGs require you to meet wagering on your deposit AND bonus so it's not kept separate.
As far as good casinos, check Casinomeister's accredited section here:
https://www.casinomeister.com/accredited-casinos/
I'm in Canada so I'm not sure which of them you can play from the US or whether you're in a banned state or not - on the accredited list it shows whether US players are allowed or not.
Hope this helps!