There are two   airports on Tenerife.  The airport operator is Aena.  Information is available from their web site.  Click here for on line  flights

If you need a Taxi, agree, if possible, on a price before the start, unless there is a metre.  You can bring a paper with the address, to avoid language problems. Read about transport in http://www.sun4free.com forum.   Else use  car hire.  It is worth, even for a few days. A trip across the island, towards the volcano of Teide, is interesting. Sometimes you have to drive through the clouds. And you arrive above the clouds. In a moon like land scape.
An alternative is to book transfer together with your hotel. This service is offered by www.alpharooms.com . An other possibility is www.resorthoppa.com  A2Btransfers.com  or shuttledirect.com

If you are planning to use public transport, the trick is to ask the tourist office at your destination. To find their address & Tel. or e/mail, use the official tourist web site for Spain: http://www.spain.info    Look in section for destinations, or use their search.

You can also consult the web site from the local bus company. It has an English version as well as Spanish. Click here