You can't "pause" the game, as the game isn't progressing by itself. Instead, it progresses only when all players agree that the game should go on, which most of the time means to pass priority. The most relevant rule to this is:
500.2. A phase or step in which players receive priority ends when the stack is empty and all players pass in succession. Simply having the stack become empty doesn't cause such a phase or step to end; all players have to pass in succession with the stack empty. Because of this, each player gets a chance to add new things to the stack before that phase or step ends.
Each time a player acts in a way that uses the stack, such as cast a spell, there's a round of priority, as defined by the rules, which (as stated above) all players have to pass in succession in order to progress.
So not only do you get to take the time to read and understand the card, but you get to think about in what way, if at all, you want to respond. You may even ask a Judge or another player for clarifications on cards or rules. This is true at all times, for example if you're simply in need of clarification of the game state.
Nothing that isn't clearly labelled as such or banned in tournament play is luck- or random-based, requires manual dexterity, or requires fast reflexes or high reaction.
In a tournament scenario, the only requirement is to do this in a timely manner ("playing at a reasonable pace") to avoid Slow Play, which means you're not allowed to stall the game by thinking about what you want to do for more than a sensible period of time in order to not slow down the tournament as a whole, or take an unfair amount of the shared round time for yourself. What that timespan is depends on the game situation, but you will always be given enough time to read a card that's reasonably unknown to you, and understand what it does.
It isn't expected of you at any tournament level that you know all Magic cards out there, however it's expected at any level that you keep track of the game state and don't re-evaluate the entire board before making a decision.
The reason you might be thinking there's a certain time limit to take action is that the Duels of the Planeswalkers games include an automatically progressing bar that gives you only so much time to react. This is supposedly done to prevent idling players from stalling the game, but has nothing to do with the paper version of the game.