On more than a few occasions, I've worn new shoes on a business trip and been miserable because my heel(s) developed blisters because the shoes weren't broken in yet. It makes for a miserable trip. Fortunately, you don't have to suffer.
Moleskin to the rescue
Several years ago, I discovered that there was a great solution to this problem: Moleskin (not to be confused with the Moleskine notebooks - they are a completely different thing). Before discovering moleskin, I used Band Aids, but they just didn't stay on very well.
Moleskin is a felt-like fabric with an adhesive coating on one side. You can find it at most pharmacies, or stores with pharmacies in them (such as many grocery stores and Target). It is in the foot care section, along with show inserts, corn pads, and things like that.
To use it, simply cut a square that will cover your blister (or the red area where a blister or "hot spot" is developing), apply it directly to the skin over the blister, then put your socks and shoes back on.
If you already have a blister, it will still hurt, but it won't get worse, and it won't hurt as much. If you don't have a blister yet, moleskin can keep one from developing.
Each day, replace the square with a fresh pad. I find that the moleskin is easier to remove if I take it off after my shower - it's waterlogged anyway at that point, so it is a great time to apply a fresh pad.
Keep putting it on there until the blister is healed, or your shoes no longer hurt your feet.
Plan ahead for more pleasant travel
With moleskin, it can pay to plan ahead. You see, moleskin is sold in larger sheets or rolls so you need to cut it -- that can be challenging these days, since it is difficult to travel with scissors.
I buy moleskin and cut it into small squares (roughly 1" square, or 2.5cm square) and put them into my laptop bag so I have some handy if my shoes begin to irritate my feet. This has helped me on at least 4 occasions I can remember, and I make sure moleskin is a permanent part of my travel gear.