Please do the following.

(1) Researching flights. Do so at the following sites:

cleartrip.com (exact dates)
cleartrip.com/calendar (flexible dates for lowest fare)
http://faresearch.rediff.com/travel/.../farenchse.htm (exact dates)
lowest-fares.rediff.com/LowestFare.php? (lowest fares for city pairs)
airdeccan.booksecure.net/Criteria.aspx (see Air Deccan comment below)

Remember to compare apples to apples, ie, full fares including all taxes. (Cleartrip quotes full fares, not sure of others.)

(2) Choosing flights. I can recommend all airlines except Air Deccan, which is often the lowest cost carrier on any route but also the "roughest" one to deal with and is boycotted by most travel agents and by portals like Cleartrip. For comparable schedule convenience and affordable fare differences, my personal preference among airlines is:

King Fisher > Jet > Sahara and Indian > Spicejet > ... all others ... > Air Deccan.

I would not plan tight connections (< 3 hours) involving different airlines. I'd also not use Deccan if any important connection or appointment was involved.

(3) Buying tickets. Having decided which flights you want, visit the India page of Make My Trip: india.makemytrip.com.

Then either chat with one of their agents (click on customer service, then chat) or call their India number. Explain to them that you wish to purchase tickets with a foreign credit card.

They will either issue e-tickets or place reservations on hold for 24 hours. They will ask you to download, fill, and sign an authorization form and fax it to them along with front and back of your card.

Two points to remember: (i) You cannot do this online as the procedure requires you to sign the form by hand. However, instead of fax you can possiby email digital photos. (ii) The authorization is for a precise Rupee amount. If you decide to buy another ticket later, you'd have to "sign and fax" again. Therefore, it is best to be plan well and buy all of your fights in one transaction

(4) Final comments. Ever since Indian travel industry started boycotting foreign creadit cards for online/phone use due to alleged fraud, I have searched far and wide for alternatives. Sometimes an individual airline, such as Spicejet, does accept foreign cards. However, for others or for complex itineraries involving several carriers, the only channel that I have found to work consistently is Make MY Trip. If a particular agent seems reluctant or lazy (very rare), just try a little later.

Make My Trip is a major travel agency and can also help you find flights, but for best results it is good to be prepared with airline and flight research of your own.

Good luck. Please post or PM your experience.