After you're able to produce a "buzzing" with your lips, you'll probably be able to play a note on trumpet. That's all we need for this tune. Don't press any piston, just play "au naturel".
Most likely you played a C, so, now count 4 beats (one empty bar) and play that note on the second bar for 4 beats.
Repeat until the backing track ends.
Here's an article on Wikipedia about swing. Check it out, it's nice, with video examples and easy theory explained very clear.
If the theory terms are a bit confusing and unknown, just try to catch the rhythm "by ear" from my example. So, listen to this one:
And here is a backing track so you can play on top of it:
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Cheers and happy learning,