Vale wrote all right things, just a more note: you can also say "Cerco di arrivare in tempo" = "I will try to be on time", for some kind of meaning is also used "cercare" to translate "to try".

Yes if you want to say "I want to try something new" in italian you would say "vorrei provare qualcosa di nuovo". "cercare" it's a synonymous of the english verb "search" or "looking for" (for example i'm looking for the keys) "tentare" means "attempt" (so it means something that you want to do but you're not sure you can do it). for esample: "ho provato un piatto nuovo" means that you have eaten a different dish in order to decide if you like it or not "ho cercato un ristorante" means "looking for" "ho tentato un piatto nuovo" means that you followed a reciped never tried and you're not sure it's good hope i'd helped you