get an indian travel agent to buy them for you

Is it important to book a train trip in advance? If so, how far in advance?

Yes, it is. Trains fill up, especially if you're traveling around holidays. If you want 1AC (personally I prefer 2AC) there is a very limited supply per train.

According to http://www.seat61.com/India.htm reservations now open 90 days ahead. You should read what seat61 has to say about wait lists. You should also be aware of the tourist quota, although I never saw a way to book that on cleartrip, and of the tatkal quota, under which some seats are held to be sold 48 hours before departure. I used that on my last trip, booking through a local travel agent in person.

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Note also that if you need to buy train tickets while in India, and you are in one of the big cities (at least Delhi or Mumbai) there are air-conditioned booking offices for foreign tourists at the main train stations. Do NOT believe the touts for travel agencies who will tell you the office is closed. In other cities you're probably better off using a travel agent rather than going to the station, although I've done both.

Also, if you are booking ahead it is worth knowing about the Indrail pass and accompanying reservations. There is no US agent for the pass, but you can buy from the UK agent, http://www.indiarail.co.uk/indrail.htm - again there is info at seat61.com

thanks for the great info and links. Very helpful.

This specific link might help the OP:
http://www.seat61.com/India.htm#Seeing India with an IndRail pass

try cleartrip.com

Try www.indianrail.gov.in
Try www.ixigo.com
Try www.seat61.com