The absolute first step is to have a twitter account. I don't think I need to help you with that but after that things get a bit more complicated.
Syndesis is using the OAuth Standard to connect to the Twitter API. On the Settings section on Syndesis it requires you to enter a Consumer Secret and Consumer Key (see Figure 1)
Figure 1. Syndesis Twitter Settings
To obtain these you must login into https://apps.twitter.com. As it did for me you may get a banner telling you that you need to apply for a Twitter Development Account before you can register any new Twitter Apps.
After applying you will need to wait till Twitter responds to you. Lucky for me I was grandfathered in and I had the syndesis-kurtstam app still sitting there and clicking on it gives you the settings for this application.
Figure 2. Twitter App Details
Figure 3. Twitter App Settings
Make sure you copy paste the callback URL from figure 1 into the callback URL here.
Figure 4. Twitter App Keys
From this screen you can obtain the Consumer Secret and Consumer Key to be used in the Syndesis Settings > Twitter.
Figure 5. Twitter App Permissions