Basically, you let the scene "ask the question" and the character actions give you the answer
If they don't even know it's magic
If they don't know it's magic at all, I go by what they do with it. They may sit down and play solitaire or poker. If you want them to sense anything at all, then after the first card, they feel a little funny. Similar, but not quite the same, as the sensation when they resist a surprise spell from a trap or unseen attacker. Then go simply by whether they continue drawing cards (ie, they are playing a game or whatever) letting them know that the sensation continues with each card. They will either stop at some point on their own, thinking "this is too weird", or they will continue until they've drawn four. In either case, the magic becomes revealed and active at that point. (Of course, if "what they do" is play "52-card pickup" by scattering the deck across the room, then they drew four and feel the magic activate at the same time they realize that only 4 actually separated from the rest of the deck or something. They quite literally toss fate to the wind, and they'll get what they get.)
Or, if they know something's up already
If they know it is magic, then it's similar, but a different feel. They will only draw the cards in an effort to determine what the deck is and what the magic is, so it's perfectly fine to ask them how many they draw. You aren't asking, "how many in your lifetime", but "how many right now". They either draw "Just one, and see what happens", and that's their choice and they get 1, or they draw "as many as I can until something happens" and that's their choice and they drew 4, or they'll give you a number. Of course, even knowing it is a magic deck, they could assume that it's just a "lucky poker deck" or maybe "a working Tarot deck" or something, and you go back to the feeling as they draw cards per not knowing it was magic at all.
To be clear-ish?
The rule doesn't necessarily require the players to specifically say "I'm using a deck of many things and drawing X number of cards". You as the DM can decide exactly how much info you give the players, and you have to often interpret their actions within the framework of the game. Many good DMs talk about Role-play vs Roll-play, because your players shouldn't say things like "I roll a search check", but instead the character should say, "I carefully look through this closet". This is another of the same thing. Telling your players, "you find an old hat, a rusty knife, and an odd deck of cards in the chest." is effectively asking the question. And the character's saying "This look like a tarot deck, I'm going to read my fortune" tells you how many they are drawing (In our case, after we spent a few minutes looking up online how many cards you draw for a tarot reading.)
The hardest interpretation is actually if your players do have an idea that something is up and are being paranoid. As far as I am aware, there's no magic or anything keeping you from looking at the deck or examining it in any way. So an interpretation I've seen is that regardless of what the player's think the deck is, it doesn't activate until they draw a card randomly.
When they think something is up, you ask what they do, and the answer is typically one of three things. 1) Fan the cards out in hand and look at them, 2) Spread them out on the table and look at them, or 3) take a card/some cards out and look at them. I try to interpret all of this in a realistic framework, and as far as I can tell, the reality of the situation is that when given any deck of cards where the backs are the same and the faces different, even that "take some cards out" option is going to be after flipping the deck over to look at faces. So a lenient interpretation of those actions doesn't call any of those three options or anything similar an activation or "draw", because no card is pulled at random, they are all pulled while seeing the faces.
But you could interpret all 3 as draws, with the first 2 being full 4 card draws and the latter most likely being a one-card draw unless they say something like "I take out the sun card and look at it", since if they don't know what the deck is then even seeing the faces doesn't necessarily make choosing a card any less random.
In our cases, though, we let the players look them over, separate them, whatever, and none of that counts as a draw. Then they most likely know something is going on and will do one of two things. Put it away and sell it/identify it later, or start experimenting as you said. Only when they start using the cards as a deck of some sort, regardless of what they think will happen, do the draws start. Then you have to interpret the experiment.
- "I draw a card and then see what happens" is an intention to draw one card. They don't know what will happen, they are waiting to make a decision about more cards later, and the deck won't allow that, so the intention is 1 card. That's always seemed straightforward to me.
- "I deal for solitaire, but slowly, pausing between each card to see if anything happens before drawing the next card" could go either way, and it's up to you. I normally interpret that the same as "draw one card and see what happens", because they are really saying the same thing, they are just adding the extra info about what they will do if nothing happens and the timeframe of "if nothing happens" is too late.
- But "I deal for solitaire and see what happens" seems more of an intention to deal the whole hand, so they would get hit with 4 cards. They aren't stating any intention of waiting between cards. "I deal for a tarot reading" would be the same thing, but would be a draw of 3 cards (or however many your group's/area's standard tarot layout is).
Couch it more in terms of precision than "gotcha"
When it gets this far with the experimentation, you may still have to explicitly ask the characters how many they draw if they either aren't being clear enough or you just don't want your characters to come back and say "but I didn't really mean that many, I was waiting to see what happens". But it isn't in terms of "ok, now you're activating something, how many do you take", it's more, "Be precise, your character is sitting down and lays out some cards, exactly how many do they lay out." At the experimentation phase, your players already know something's going on, so asking the question in this way isn't giving anything away, it's merely asking for clarification of the character's already stated actions. You would ask a very similar question even if it was a completely normal deck of playing cards and they said "I'm going to deal poker". "Well, is it 5 card stud, 7 card stud, or what? I need to know the odds."
Long story short
Make it fun. You don't even HAVE to have the cards take effect immediately, if your player is drawing cards simply to look them over, just let them draw one, and tell them what it looks like. Then see if they draw another and see what it looks like, etc. If they go through 4, then they activated four and tell them what happens. If they got bored after 2 and put them away, or start to hand the deck off to another player, they drew two and let them know what happens. As long as the first player's draw goes into effect so that that player knows what's going on and so that the other players know what's going on (if the card effect allows that), then you aren't changing the outcome by having the effects come up after the player has made all of their draws instead of instantaneously as they draw. Even the interpretation for "must be in one hour" isn't giving you an hour to decide, since the rules make the character decide before the draws start. At best, it's giving you an hour to recover from whatever the last card is. So if you think that hour would help, this exchange is taking a short enough real-time that it's not a big deal to even back it up and say, "Ok, you are drawing 2 cards, but when you draw that first card, X happens. You know that you will have to draw the second card and don't know what it will do, but you don't have to right now." You still haven't told them what that second card will do, so you're really not making much difference, but you've allowed the character's mostly unbiased actions answer the question for you and you are being fair to the player by still allowing them all of the options the deck's rules allow. (Of course, something I've never thought of, since the deck will effectively draw itself after an hour, a character could intend to draw 2 cards and the first one kills them, but the deck draws the next one an hour later anyway. If the first card is immediate death or turned to stone, but the second auto-draw an hour later is 3 wishes, can you wish to cancel the first card? In death, you could theoretically be making your wish from the afterlife, but I forget how conscious you are if you are stoned.)