How do I introduce a new game to kids without frustrating everyone?

Teach the goal first, mechanics second
Start by explaining what winning looks like and why anyone would want to play. Then introduce only the mechanics needed for a single turn—nothing else. Avoid rules about rare situations until they come up. This prevents players from memorizing 20 facts that won't matter for 30 minutes.
Play a few turns before full freedom
Conduct two or three supervised rounds where you actively narrate what's happening and why. This gives everyone a mental map. Then hand over control. Players will ask clarifying questions as situations arise, which is normal.
Keep the rulebook accessible
Don't recite rules from memory. Point to the rulebook and read the relevant section together when questions emerge. This teaches kids that rules are references to check, not commandments to memorize.
Expect slowness and restarts
Accept that the first play will be slower. Some groups restart after the first turn once everyone understands better. That's fine. Learning is the point, not optimal play speed.