Best Answer - Chosen by Voting
"here" ---> "Aquí", e.g. "¡Aquí esta Juanito (Johnny)! (starts chopping down door with axe)
"There" ---> "Allí" (if you mean a specific place), "Allá" (if you don't mean an specific place). Sometimes they can be used as synonims without a problem, but "allí" usually indicates more closeness in space than "allá". Also, allá admits distance comparisons, allí doesn't, e.g. "más alla" (more over there), "¿tan allá?" (So far?)
E.g.:
Allí:
1. Dejé el libro sobre la mesa. Busca bien. Está allí. (I left the book over the table. Search carefully. It is there)
2. ¿Estás allí? (knocking the door: Are you there?)
3. Dejálo ese allí (put that one there, pointing to the table). El otro déjalo allá (Put the other one over there, pointing to a farther location)
4. Estaré allí pronto (I'll be over there soon, where the other person is). Voy para allá. (In this case they mean the same)
Allá:
1. Állá en Inglaterra está amaneciendo (Over there, in England, it is dawning). In this case using allí would sound awful.
2. Allá toman más té que aquí (Over there, people drink more tea than here)
Regards,