The main airport of the Seychelles is SEZ which is on the largest island of Mahe.
Using points, here are the main ways of getting to SEZ, which are rather limited:
American Airlines: Using their partner Etihad Airways who fly from Abu Dhabi (AUH). Seychelles is in the Africa zone, flights from AUH are 30k each way in economy or 45k each way in business. Unfortunately flights from the USA or Europe to Africa cannot connect in the Middle East zone (where AUH) so you would need a separate reward to get to AUH from the US or Europe
Delta Airlines: Using their partner Kenya Airways (KQ) is now probably one of the best ways to get to the Seychelles. They have three times a week service from Nairobi (NBO). To get to Nairobi KQ have multiple daily service to and from London, Paris, Rome and Amsterdam and you can get onward flights to the USA from there. Availability is generally quite good in both coach and business class and can be checked by creating a FlyingBlue account at www.airfrance.us.
United/US Airways/Star Alliance: Star Alliance member Ethiopian Airways offers four times a week service from Addis Ababa (ADD) in Ethiopia. Availability can be checked at United.com and is generally wide open in coach but very stingy in business class. However it is only a four hour daytime flight so coach is not too bad. Ethiopian offer onward non-stop flights to the US (Washington DC IAD) using the 787 Dreamliner and availability there is generally very good, and the US flight gives good connection times to the connection to Seychelles leg. (Note: this service is ending in March 2014)
Chase Ultimate Rewards: By converting to Chase partner Korean Air you can theoretically redeem on Emirates. Round-trip from Dubai (DXB) is 35,000 miles in coach, 70,000 in business or a nose-bleed 105,000 miles in first class. Again for a short four hour or so connection, coach or at most business would seem adequate.
American Express Membership Rewards: Membership Rewards can also be converted to Delta or Air France for Kenya Airways.
Starwood Preferred Guest Points: Convertible in increments of 1:1.25 in amounts of 20k at a time to ANA for Etihad (with fuel surcharges), or directly to Emirates or Etihad for redemption with them.