Welcome to the forum and Portugal.
I copied this from another site so cannot claim authorship.
http://www.visitingeu.com/western-europe/portugal/2008/04/how-to-get-from-lisbon-airport-to-city.html

Hpwever you will need to be specific about which hotel you want. Most are scattered around a large area of the "centre" called "Avenida da Liberdade". As the actual center is to the soiuth of this avenue and is recognised as Estcao do Rosio; which is a large square. You woundn't want to be dropped off there as from there its up hills at every corner! apart from the end which goes down to the Tagus.
Rosio is a good place for restaurants though, but beware of beggars and pick-pockets.

Great that Dan,it is all i need to know
thanks again

I was going to say Dan's info will be deleted for copyright issues - but it was whilst I was typing.

More seriously, that link is not wholly accurate and misses some important facts relevant to your enquiry.

1. To avoid being ripped off by taxi drivers you can buy a prepaid voucher at the airport info desk. But if the hotel is in the cluster near Entrecampos station this may be more expensive than an honest driver, if it's in the Oriente district it's not worth it.

2. The fare for the slow bus is €1.40 for a single journey. On the 91 or 96 it's €3.50 but these tickets are valid as day passes on the entire Carris scheduled network (not the special tours with commentary), that's the yellow buses, the trams and funicular railways and elevadores that climb the hills in the old town. So if you land early enough to do some sightseeing that day you can get more out of them. Full info on public transport in central Lisbon is at http://www.carris.pt/en/home/

Useful routes for tourists, Bus 37 from Praça Figueira which takes you up the very steep climb to the castle. Trams 28 and 12 which run around the old town areas. Tram 15 out to Belem.