If you are there when the plan starts to happen, it's fine to assume the plan is including you:
Let's all go to X right now! (Or tomorrow, or when exams are over)
Great idea! (Ask more questions if necessary.)
If you were not there when the plan was made, but two people discuss it in front of you, it's fine to assume they wouldn't mind if you come, but best not to assume you can invite yourself. Showing enthusiasm is the way to go here.
That sounds like a great time!
If they want to invite you, they can easily say "join us" or "it sure will be, are you coming?" or the like. If they don't, they can just say something noncommittal like "sure will be" or "yes." You can respond as you would if someone was telling you their plans for their vacation - friendly interest and encouragement without assuming they will bring you along.
If you weren't there when the plan was made, and people who are going aren't discussing it in front of you, but you hear from another person "X and Y are going bowling tomorrow" then it's just slightly trickier, because you need to discuss it with X and Y, not the person who told you, but the subject hasn't naturally come up with X or Y yet. Nonetheless, you can take a similar approach.
I hear you're [activity] [timeframe]. That sounds like a great time!
Again they can either agree that yes, it sure will be, or they might ask if you can come too. Even if they don't, they know now how you feel about that activity, so if they do it again, perhaps they'll remember that and invite you on the next one.
Of course this works best when you're aware of the sorts of things to which invitations are quite exclusive: vacations, dates, weddings etc. That way someone doesn't end up saying something like "sorry, but it's really kind of a date thing - just the two of us - hope you don't mind" which would be super embarrassing.