One short answer is: as often as possible.
Another specific short answer is: once a week.
Chess is about experience, not just knowledge. It's different from a test. You can make progress, or you can regress. A few tournaments may not reflect his/her true strength. It depends on too many things: his/her opponents, his/her mood, his/her psychology, his/her time management, etc. Only playing more can smooth these out.
Often a parent wants to see the result right away. After three tournaments, s/he will start to complain about his/her child's non-progress. The more you want to hurry, the higher the pressure your child will have, and the worse s/he might perform.
If your child treats tournaments as big tests, such as SAT, which might impact her/his chess career, then s/he will feel greatly pressured, and s/he might flunk the test. Failing is normal and losing games is normal in chess. S/he should think about tournaments as small quiz. Passing or failing will not impact anything. S/he could always try it again, and again. Every week s/he will have a chance to try again.
Making tournaments as her/his routine, just like s/he takes lessons. Then there will be no important decisions coming from their results, and no struggle. Just go and play. Sooner or later, you will see the improvement.