First Option: Planning ahead
It's best to check ahead which events will take place when you're in Berlin, because sometimes you'll need to order your tickets in advance (e. g. for the concerts of the world-known Philharmonic orchestra or for the good opera productions). The simplest to check that is by searching Berlin's official tourism website.
To go there, please open the following link:
All you have to do now is to fill out the relevant dates:
You'll then be presented with a results page, where you can refine your search according to various categories:
Clicking on one of the events your search yielded, will lead you to the event page with all the relevant information (including address etc.). If it's an event that requires the purchase of tickets, you could do that with your credit card using the following button:
This button will take you to the website of the German company Eventim. This is a very known and reliable company that specializes on selling tickets over the Internet. On the new page, you'll see a list of dates for the selected event. You then need to click on the button next to the date of your choice:
From here on, the process differs from one event to another - basically, you should select the kind of tickets you'd like to buy (most places/events offer tickets in different price categories), the number of tickets you require, and finally complete the purchase with your credit card.
► The official website described above is naturally not the only one selling tickets for local events (for the sake of earning a commission), but the other websites are in German, so they probably won't help you. But there's an alternative in English, namely the events section of Berlin's English speaking magazine, called "Exberliner". They tend to focus on events in English (for the ex-pats in Berlin) and on alternative culture. You can use the calendar on their website to fetch events on a specific, future date:
► And then there's iHeartBerlin, whose target group could be described as "hipsters":
► You might also want to check out the following website of the Berlin association for Stage art & performances. Although many productions are meant for the local German speaking public, some of them are suitable for tourists too:
Second Option: Last minute tickets
"HEK Ticket" is a company that specializes on last minute tickets, typically as of 2 pm before the evening of a particular event. They have offices you can go to, for example at Alexanderplatz (on Karl-Liebknecht-Straße, across the Alexanderplatz S-Bahn train station). You might also want to wander around their website and see what they offer in different categories (classical concerts, opera, etc.):
(you might need to change the language setting at the top right corner)
Last but not least...
...if you have more questions on special events in Berlin and how to get your tickets, we'd be happy to advise you personally.