My plane lands at Guangzhou Baiyun Airport at 10p.m and i need to go to Foshan Hospital.

Dear Alice, metro may be an option, and your timing may catch the schedule. However, it requires several transfers on the way. Considering all, intercity bus is suggested. It is scheduled till very late and the last one even leaves at 01:30 the next day. Board the bus between Gate no. A1-A4 or No. B11-B13. It takes around 70min and the bus fare is CNY31. Upon getting off, take a taxi to the hospital.

thanks for the reply. Where can i take the intercity bus?At the airport or nearby? Will i have to change station for the intercity bus?And at this time, is it safe...particularly for a young woman? Also, how can i spot a safe taxi at this time?

The intercity bus station is at the airport between Gate A1~A4 or B11~B13. It will take you directly to Foshan without stop in the midway. It is suggested you take the intercity bus, which is safer than hailing a taxi. No worry!

ok thanks. intercity bus sounds like a very good idea but the problem will be when i arrive to foshan. Can you please tell me the address where the intercity bus will stop? I will try to google my options from the foshan stop to the hospital?Please

One bus route to Foshan will arrive at Lanshi Metal Exchange Center on Kuiqi Rd,Chancheng District.
The other one will go to No.123 Gaomingdadao Rd, Gaoming District. The bus will stop at Huameida Hotel, at No. 61 Middle Boai Street, in the midway.
Hope helpful!

Ok, i guess my only option is to take a taxi upon arriving in foshan. Now, the big question is "how do i take a taxi?i mean, are there safe taxis at this time(1am) and how do i know they won't scam me?"

The taxi is still available at night. Those normal cabs have 'taxi' signs on the top and are metered. You should notice that.
Or, if you really feel worried, you may consider spending one night in the hourly lounge at B1 of the airport terminal. Take a coach to Foshan on the next morning.