How do I build beats in Logic?

That's a very basic question. I would suggest to get used to the concept, you import one of Logic's many drum loops into the arrange. Please make sure it is a "green" loop with MIDI data and not a "blue" audio loop which only contains the ready-recorded waveform.

Now open up this loop in the piano roll editor and look at the MIDI data inside it. You should see there's a certain pattern of MIDI events triggering the different drums.
Try to add an event here or there and listen to it to see how it changes the beat. Or remove some of the events.

Now with ultrabeat, you best use the step sequencer that's built inside it. You have to switch to the step sequencer view. Now you can click on the pattern to add or remove single beats.

Try around a little bit to get used to it.

Fox