Your gateway town to Hampi is Hospet , bustling town located very close to the Hampi village. This is the major travel hub from where you can get the travel connections as well as a variety of hotel options. There are good road and rail connections from Hospet to a number of major towns and cities around this part of India.
By Train
Some of the long distance express trains pass via Hospet. There are a few passenger trains that connects Hospet with nearby cities.
If you are coming from far places to Hampi ( like Chennai, Mumbai , Bangalore, Delhi , Kolkata etc ), look for a direct ( or even split journey ) train connection from your place to Hospet Jn ( HPT) . Hampi is a short bus ride from Hospet town.
Direct trains include Hampi Express (Hubli - Hospet - Bangalore - Mysore) ; Amaravathi Express(Goa - Hubli - Hospet- Vijayawada - Vizag - Bhubaneswar - Kharagpur - Howrah) ; Haripriya Express (Kolhapur - Belgaum- Hubli - Hospet - Guntakal - Tirupati ) ; Garib Nawaz Express(Bangalore - Guntakal - Hospet - Hubli - Belgaum - Pune - Kalyan - Surat - Baroda - Ahmedabad - Ajmer ) ; Hyderabad - Kolhapur Express (Kolhapur - Belgaum - Hubli - Hospet - Guntakal - Raichur - Hyderabad ). This is only a brief list, there are a few more trains via Hospet.
Another strategy is to get connections from Hubli or Guntakal . Hubli Jn (UBL) and Guntakal Jn (GTL) are two major rail junctions west and east of Hospet ( Hampi) respectively. May long distance trains pass via these two stations. You can look for a connection from Hubli or Guntakal to Hospet.
By Road
The state run KSRTC operates (www.ksrtc.in ) a number of schedules from Hospet to various towns and cities in Karnataka.
There are even a few interstate services connecting the cities of neighboring states (services to Goa, Andhra Pradesh and Maharashtra ). Though not as comfortable as the train journey for the medium distance travel, you can opt for the bus services.
Apart from the state run KSRTC a number of private operators too run regular long distance bus service to Hospet ( and to Hubli , a major town 3 hours west off Hospet), Plus check out with your local private bus services if they run any services to Hospet.
Then of course you can drive all the way to Hampi ! Take NH13.
By Air
Hubli is the nearest airport (about 160km) west of Hampi. Further northwest is Belgaum airport (about 270 km from Hampi). Both has moderate connections with cities around the region. A more practical option is to fly to Bangalore and take the Hampi Express. Bangalore is connected with all major cities of India. Also Bangalore has many international connections. By the way Hampi Express stops at Yelahanka (YNK) station, closer (20km) to the Bangalore airport. (You'll save 1 hour travel to the city stations). If you are doing an onward/return journey to Hampi (Hospet Jn) from/to Bangalore airport, this can come handy.