This page helps you get to the hotel.
Faro is a small city, so not easy to get lost yourself ;-).
From Airport, take Bus 16 direction "Faro Bus station". The other direction is "Praia" (means beach), just make sure you jump on the bus that goes in the right direction. In Portuguese, "linha" means "line", just in case you find any sign refering to "Bus Linha 16".
Ticket costs 2,25 Euros, you have to pay in cash to the driver.
Your trip takes ~20 minutes, you have to jump off the bus in the last stop at the Faro bus station. Then, walk ~10 minutes to the hotel.
For more info, see the unofficial Faro bus timetable website.
If you arrive by train from Lisbon (or somewhere else in Portugal), you have to jump off the train at the Faro train station, that is located next door the to the Bus train station. You have to walk ~10 minutes to the hotel.
You can also take a taxi from Faro train station to the hotel, of course.
There's a taxi stop outside the terminal, the ride should costs you ~10 Euros and it takes ~15 minutes.
Before you drive into Portuguese highways, make sure you buy your toll card online. Otherwise, you risk to get fined by Guardia Republicana (Portuguese police). From Seville (Spain), I usually pay 6 Euros to go back and forth, so I have to buy a 10 Euros ticket. They will keep the 4 Euros left that you can spend next time you come back to Portugal with the same car ;-). Actually, it is even possible to check how much budget you have left online, I don't remember where the link for this is though.
If you drive in A22 highway, you have to take "Saída 14" (Exit 14) to Faro.