There's no airport in Albufeira, so the easiest way to get there is through Faro Airport. There are couple of different ways for transportation between Faro Airport and Albufeira. One of course is regular buses. The cost is something like eur 1.60 (I might be just a bit wrong) for a bus from Faro Airport to Faro and EUR 4.50 from Faro to Albufeira. You could take a train from Faro to Albufeira as well, that's EUR 2.50, but it doesn't make much sense as you'd still have to take a bus from Albufeira train station to Albufeira bus station. Once you're in the Albufeira bus station, you need to choose another line to get to where you actually want to go.
Another way to travel between Albufeira and Faro airport is using airport transfer services (for a specific one, search the internet), the cost is anywhere between 30 and 70 euros one way. If you're traveling alone, better take the usual bus. But if you're in a company of 4-9, the fare I gave you is per bus and it makes sense to use the airport transfer and the cost per face ain't big, plus you can use it during the night as well. The last regular bus from Albufeira to Faro goes at 8 or 9 pm...or something (search the internet, you can find the exact times), so if your flight leaves at 7am, airport transfer is the way to go, whenever possible.