At around 25 minutes into Game of Thrones S08E03 Jon Snow and his dragon (Rhaegal) were resting on the wall of Winterfell when he could have been burning the army of the dead whom the living were fighting and struggling against. Or most importantly, he could have lit up the trench. Why wasn't he doing either these things?
Because that was not the plan. In the war room scene of episode two they basically admit they cannot straight out defeat the army of the dead. The plan is rather to put up a good fight and lure the Night King to the Godswood in Winterfell, by using Bran as bait. There they would kill him and hope that destroys the whole army. So Jon is waiting for the Night King to take the bait, rather than flying out and risking the plan to fail.
However, after Dany sees all her Dothraki massacred she basically abandons the plan and attacks anyway. Jon shortly protests against this ("The Night King is coming") but joins her anyway.