Travelling to Goa from outside India is easy. There are some direct flights (e.g. Qatar Airways). Alternatively you can fly in to Mumbai or New Delhi and take a short domestic flight to Goa. Full details should be available on any good travel agency web site. Book early to obtain reasonably priced flights!
Visitors to India generally require travel visas. The procedures for obtaining visas have been streamlined and made more efficient with the new electronic visa application system. Please check your respective Indian High Commission/Embassy web sites for further information. It is advisable that you seek tourist visas for India for which you may not need any invitation letters but only hotel and travel booking confirmation. Please check for details.