Usually when I travel I buy online well before I travel and try and stay with Kingfisher air.
website: www.flykingfisher.com
For sectors that due to schedule or high price, then I try and book on the discount carriers goair or spicejet.
One can book online using a US Credit card - have seen Amex is pretty easy & convenient. With Visa ... due to higher fraud rates, sometimes it becomes difficult and one has to input bank details etc.