By Air
It's not possible to fly direct to Reunion from the UK, Canada, the USA or Australia. Travellers will need to connect in Europe, usually Paris, or in Singapore for those flying from Australia. Air France are the main carrier flying into Reunion's Roland Garros airport.
An alternative is to fly to Mauritius and catch one of the short flights between the two islands with Air Mauritius; British Airways fly direct to Mauritius from London, and Emirates fly direct from Dubai.
Expect to pay around £500/$1000 - £700/$1400 for a return flight.
By Boat
It's possible to travel from Mauritius to Reunion by the ferry 'Mauritius Pride'; the overnight journey takes around 12 hours and will cost around £70/$140.