"ya" means "now"... "todavía" means "still". In the negative way, "ya no" is "not now" or "not .. anymore" and "todavia no" is "not .. yet"
For example:
"ya puedo viajar" => "now I can travel"
"ya no tengo dinero" => "I don't have money anymore"
"todavía puedo viajar" => "i can still travel"
"todavía no tengo dinero" => "I don't have any money yet"
I was thinking about this, and I came up with a "general rule" to decide when to use "ya" and when to use "todavía":
In the negative:
"ya no" is used when an action was happening on the past an now it's not
"ya no tengo un automovil" means that once you had a car but now you don't
"todavia no" is used to express that the action wasn't happening and it's still not happening now. It also implies that you're planning/waiting to do the action in the future
"todavia no tengo un automóvil" means that you didn't have a car and you still don't have one and implies that you're planning to get one
In conclusion:
"ya" (as adverb) is used to express a complete change on the action "ya soy", "ya tengo", "ya no puedo"
"todavia" is used to express a continuity of the action "todavía soy", "todavia hay", "todavia no sé"
Hope this was clear =P (sorry if I missed some accents)
Edited
"ya" is more than an adverb..a few other usages:
- It could mean "ok" or "yes" when answering a question.
quieres salir esta noche?
ya
- It could mean "yet" when it's in a question.
"ya saliste?"
listos....YA!
For more information, check its definition in a dictionary ... ya? =P
ya
cuando me preguntan por algo que tengo que hacer para dar a entender de que ya estoy enterado.