Sorry, you can't catch it in HG/SS but you can catch it in Pokemon Platinumand here is how to do it.
1: Get the National 'Dex.
2: Go to Route 229 (only reachable after getting National 'Dex.
3: Go to the small pond in Route 229 and MEW will be floating above it!
4: It will be at Lv. 30 (like Pokemon Emerald's Faraway Island event.
5: I think MEW lives here because it is a rainforest like Faraway Island and in one of the books in the Pokemon Mansion it says: In the middle of the rainforest, we discovered a new Pokemon, we christened the newly discovered Pokemon "MEW". MEW gave birth. We named the newborn MEWTWO. It's powers were too powerful to keep balanced.
6: That is the story of MEW and MEWTWO.
yes
An event
yes
you can't
Mt.Moon
Mew can't be catched in Pokemon heartgold, only mewtwo.
You catch Mew-Two
You can't catch a Mew in the wild. You'll need to trade for it or use the Action Replay.
You cannot catch a mew. You can only get it through events or cheats.
You can't catch it at Pokemon Pearl, you'll have to Transfer it from LeafGreen/FireRed or trade it with SoulSilver/HeartGold
U can't in heart gold but u can catch mewtwo
you need action replay go to youtube to get the code