What to do if an emergency arises while traveling...?
Many destinations popular with tourists have a *"Tourist Police"*...that would be the first place to go... They likely handle your kind of problem regularly...and can direct you to the next step... Supposedly these Tourist Police have some language training...mostly in English...the universal language of tourism now...
The next place to check might be in *any large hotel...at the desk*...they are used to problems coming up and can give good advise...even if you are not staying at their location...English skills are usually better there as well...
It is a good idea to seperate your ATM, credit cards and cash...into at least two locations...so the loss of one will not create a doomsday scenario... Remember losing one ATM card is a problem...losing all of your ATM cards is a disaster...!
You might leave some of your credit card and ATM data with someone at home...who could handle needed notifications if you are in a remote location...
Likely a lost passport will eventually be handled by the local embassy...so it might help to know the address and phone number in advance...
As to medical emergencies...your hotel desk is the best place to start... Desk people are used to tourists having problems...and they live locally so they probably know of the best and closest medical facility and can get your a good reference...and a taxi if needed...
This by the way is a good reason for staying in "real" hotels or hostels...and not renting an apartment... When you rent an apartment for your lodgings..there is often no one to call...and you are pretty much on your own...
The best way to handle emergencies is to be prepared and avoid having one in the first place...