Is there a way to check that the conditions on your plane ticket are actually what your travel agent said they are?

Yes. There are two ways:
1. When you get the confirmation of your ticket you should get also the fare rules conditions (restrictions). Ask your travel agent where yu can find them.
2.You can contact the airline.

Once the booking is made, ask the agent for the “booking reference” or “booking identifier” for the airline. There might be two such numbers, in the case of a code share. For example if a US travel agent buys a ticket from United for an Air Canada flight, there will usually be a United booking reference and an Air Canada booking reference. Booking references are usually 5 or 6 letters or numbers; you can use them to check in online and sometimes to make changes without getting the travel agent to do it.

As soon as you have a booking reference, go to the airline web site and try to “manage my bookings” or “manage my flights” or “see future travel” or whatever it’s called by that airline. Much of the time you will be able to see your fare class and fare rules this way.

Your fare rules depend on which airline issued your ticket. You will sometimes hear the words “stock” and “metal”, as in “I’m on United stock but Air Canada metal”. Stock refers to the paper that was once used to print tickets, and metal refers to the actual airplane. You can find out your stock from the ticket number. This is a long string of digits labelled ticket number or e-ticket. It’s super important to have with you – many times I’ve had issues checking into Lufthansa-operated flights on an Air Canada ticket and have resolved them only by bringing up my ticket number. The first 3 digits identify your airline – 014 for Air Canada, for example. http://www.iata.org/customer-portal/Documents/ireland-airline-listing-may-2011.pdf seems to be a helfpul resource for figuring out whose stock you are on.

In general, if you have a 3 digit flight number (LH 123) then you are on that airline’s metal. If you have a 4 digit flight number you are usually on someone else’s. It doesn’t really matter, because the ticket stock governs the change rules, you just might want to know for other reasons, like going to the right terminal (I’ve gone to the Air Canada part of the Las Vegas airport, only to discover my United-operated flight left from a completely diferent terminal) or qualifying for an upgrade. The 3/4 digit rule isn’t universal. If you’re not sure, try searching for a flight between the two cities on the website of the airline that is issuing your ticket. If you don’t find your flight, try other airlines based in either the departing or arriving city. When you find a flight between them that matches your times, you’ve discovered whose metal you will be on. This can also help if you have only one booking reference – you may be able to look up your booking on one airline and get the other booking reference that way.

If your booking reference didn’t help you to find fare rules, then your last resort is to look for random strings of letters (sometimes labelled fare or class) in the confirmation you got from your travel agent. The first letter is the fare class (Y is popular for the most expensive economy, J for the most expensive business, but different airlines use different letters) and the letters that follow identify specific subclasses or charges (eg $150 for a same day change) that apply to the ticket. Doing some searches for your specific airline should help you decode it. Alternatively you could call the airline and ask them to help. That said, I just ran through emails from the last few years from 5 different airlines (some from travel agents, some from Expedia et al, some from airline web site bookings) and every one of them had the fare rules in words. And those are probably the “bottom line” when it comes to being sure. More than a piece of paper your TA hands you.

The surest way, which won’t make you happy at all, would involve reading the ‘Fare Rules’ document when you are making a booking. This is a document separate from the terms of carriage of an airline which lists general conditions, usually mentioned as a footnote or a link at the payment stage. This document lists all charges associated with your specific series of ticket. The key sections I look at usually are layover terms and cancellation terms: often I’ve discovered I can break my journey on layovers for a couple of days for free at no or minimal extra cost. Also, some airlines have more generous cancellation policies than others so when I’m doing flight comparisons, I tend to follow through to an airline site till the last step just to compare this section for a couple of flight offers.

Is there are way to check this after a booking has been made? Not that I know of, unless it’s calling up an airline to ask them specifically about a point you want to find out more about.