An ostinato is a repeated rhythmic pattern. One pattern is fine, but when you combine two or more together, it gets interesting - and people like interesting rhythms, not boring, predictable rhythms.
We can write percussion ostinatos on music paper just like any other instrument - with a few exceptions. For example, most drums don't have notes. They are called unpitched instruments (a pitch is a note).
Here is a sample of how musicians would write their rhythms:
We can do this with software, online webpages, or with pencil and paper.
Useful for writing ostinato patterns is the repeat symbol that goes at the end of the line:
Best of luck writing your ostinatos!