You can get them from veilstone city department store. you can also get them underground when you trade in dug up items.
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from dawn ( choose right hand )
just google it it's not hard
go to key items find it and hit use save and your in underground
you get an explorer's kit from a guy in a hous ein Eterna city, go outside, go to key items, click it and you will go underground.
You can't store items on Pokemon Diamond and Pearl, as your bag now can carry an unlimited supply of items.