Building your audience on Twitter is a bit different than on Facebook.
Let's look at what you need to do:

The Location and Language selection is pretty self-explanatory - Simply add or exclude the countries and languages you want in your Audience. 

Gender is pretty clear as well, you can decide to include both in your audience, or have an audience including only one (or two audiences including each gender separately). 

The Age selection is a bit different from Facebook one: 

Then, you can add some Detailed Targeting for a more precise audience that would fit your needs. Amongst the options, you'll find the Interests - selecting at least one Interest is mandatory to get the estimated reach for your audience! 

You can add an Event to your targeting: 

Choosing to target an event will enable Twitter to push your ad to people that are tweeting about the event. They will automatically target people that are positively talking about the event they're attending! You can read more about it here!

Finally, let's look at the placements available on Twitter: 

The Timeline one will display the ad as it it were a regular Tweet, with the mention "Sponsored" under it.
The Profiles and tweet detail pages placement is going to promote an account in the suggestions for new subscriptions to users.
Search results will display your ad for specific searches. 

You also have access to advanced placements: 

In there, you can separate users based on their operating systems, devices, networks, or connection types. 

Once you're done, don't forget to add the Audience, and you can move on to the next step, Creatives

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