For travelling to Coimbra you can use either the airport of Lisboa/Lisbon or Porto/Oporto. Although Lisboa has more connections to European capitals, Oporto also offers good connections. From either airport you can use the metro (running every 5-10 min in Lisboa and every ~ 15 min in Porto) to the railway stations of Oriente (Lisboa; 5-10 min) or Campanhã (Porto; ~ 40 min), respectively. Then you take the fast trains (AP or IC) to Coimbra (1h35 to 1h50 from Lisboa or ~ 1h from Porto).
Metro tickets could be purchased at the respective stations (buy two trips in case you plan to use the same means for the return journey) and keep the ticket (later you can also top it up).
Trains run most of the day time about every hour. Trains tickets may easily be purchased at http://www.cp.pt/passageiros/en/buy-tickets (advanced purchase may profit from a reasonable discount).
From the Coimbra railway station (Coimbra B) to the Hotel or the Department of Physics, a taxi (less than 10€) is the best option.
If you are travelling from the Lattice conference in Granada by air, a stopover in Madrid is mostly required. Note however that there is also a direct flight to Lisboa from Málaga. An alternative is to rent a car and drive the ~700 Kms between Granada and Coimbra.