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Any produce that hasn't had trumot and maasrot taken from it needs to have it taken before it can be eaten, once it's been brought inside. (If you're eating them straight from the plant as a snack, it's considered "achilat aray" and doesn't require tithing.)

When taking trumot and maasrot, there are a few considerations: there's the Trumah, which is designated for a Kohen  can't be eaten by non-kohanim; there's the trumat maaser, which is the Trumah taken from the maaser (and has the same state as Trumah); and the maaser sheni / maaser Ani, which has to be either taken to Yerushalayim or given to the poor, respectively.

When taking trumot and maasrot from tevel vadai - produce that definitely hasn't been tithed - you take with a bracha. You remove a certain percentage (I don't remember what exactly and can't check right now) and double wrap it before throwing it out. That's the Trumah and the trumat maaser. As for the maaser sheni, most people designate a coin that's the "maaser sheni coin", transfer the status of maaser sheni to the coin (there's wording for this but the precise wording isn't that important), and then either spend that coin in Yerushalayim or toss it into the dead sea.

For D'mai - you don't know if it's been tithed or not - it's the same process without a bracha.