TL;DR:
"+2 Actions" does not mean "play 2 Action cards". It means "add 2 more to the number of actions you are able to play this turn", or "add 2 to your Action pool". So you draw 1 card, then add 2 to the Action pool, then decide if you want to discard your hand for a new one or not... then regardless of which you choose, you still have 2 more Actions left than what you had previously.
Long story: (an excuse to eat a lot of candy)
When I teach the game to newer players, I sometimes use candy. You start your turn with 1 Action (in the Action pool), which is 1 chocolate chip in front of you when you start your turn, and 1 Buy (in the Buy pool), which is 1 marshmallow in front of you when you start your turn.
In your Action phase, you put 1 chocolate chip away (usually eat it) when you want to play an Action card. If it gives you +1 (or +2 or more) Actions, you take that many more chocolate chips. Then you know if you can play another Action card still or not... especially important once new players get into the combos of villages and dead actions. But it's important to know that something like Throne Room, which says "play an Action card from your hand" does not use up a chocolate chip to play the next Action since it instructs you to do that (which is distinctly different than saying "+1 Action", which means add 1 chocolate chip in front of you).
The same goes for Buys (marshmallows). Any time you get +Buy, it doesn't mean you buy something now with the money you have... it means add a marshmallow to your pile. Then in your Buy phase, you know how many things you can buy, and each time you buy something, you eat a marshmallow. Again, more that "gain" (e.g. Workshop) does not use up that marshmallow.
Then during clean-up, all chocolate chips and marshmallows disappear (get eaten!) at the end of every turn. (This concept is important for some reactions that can give you +Action on other people's turns, which do not get saved for your next turn).
You could also use skittles for coins. Generally, I don't, as the introduction to coins doesn't require the full complexity of understanding the rules of coins. But it can show the importance of playing treasures one at a time (e.g. Bank), abnormal coin usage (Storyteller, Black Market), or even tracking as you move between phases (e.g. Cavalry, and note that marshmallows are important for this one too). Any +$ on Action cards gets you that many skittles (you start your turn with 0 of these), then treasure cards each generate a certain number of skittles. To buy a gold, you eat 5 skittles and 1 marshmallow (unless cost reduction cards are in play). Again, all skittles disappear at clean-up (of every person's turn). Skittles are different than coffers, which do not disappear at clean-up.