How do people train so fast say someone has a 4k one day they have a 5k the next day how do you?

They probably train using the mystery trainer where they get lots of exp hence they level up quicker

wat is the best move vs him (not tm's )

Well first people need strong pokemon like level 2000 or 3000s so that the opponent trainers are the same/stronger lvl than your highest pokemon and they make low level pokemon battle the high level pokemon

You get a poke( if your a beginner) and you teach it it bolt strike and fight swimmer Richard with bolt strike

heres what u do u need a very high lvl Pokemon that u don't want to use in your party u need one of that, 4 golurks or gollets and the Pokemon u want to train, all the Pokemon must have blizzard and bolt strike
first u must fight the bird trainer use a golurk or golett hurt it until its hp is at 4,5 or maximum 12 is u are training a lvl 5 Pokemon if u aren't using a lvl 5 Pokemon it doesn't matter because it makes no difference but when the Pokemon reaches lvl 500 or 600 just fight zapdos the legendary Pokemon at the npc fights menu zapdos lvl is way higher than your high lvl Pokemon by 4 or 8 times ( i forgot lol) but most of its attack cant hurt golurk but one can that is night shade
how does zapdos learn night shade ??? so u know how to do it u can try it out yourself

it is pretty easy bro some may blott nevermind them
some like lee and mat and such sorts of hardcore trainers train against mystery trainer in the town section using a golurk with toxic

if you want then you can fight swimmer richards and use electric moves on him or fight bird tamer and use any ghost type pokemon coz he doesnt have any effect on ghost pokemons

battle wit mysery trainer u can earn more exp than towers etc.
the moves u should use against mew is :-
1. use toxic form ur first sot poke
2. when it gets pois
3. use megahorn etc ..

Best way to train is get a high lvl poke and train at mysterious trainer.
First, you toxic its mew.
you get a full team of golurks with fly to ensure success.
toxic with your main pokemon and switch to golurks and fly like mad.
wait until mew is on low hp and will die next turn from poison and switch to pokemon u wana train to finish it off. you get tonnns of xp from doing this.

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Read that guide. It explains better than people with no education.

as biga says yes read the guide bro ..and have a gollet/golurk so that u can get something high

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alot of people have others train for them, or they use the guy in the ally