I wear heels every single work day, and I have a busy job where I walk at least 10k a day, often closer to 20k. My advice:
Never wear 'stiletto style' heels and/or pumps for longer walking. Only wear them around the office or on short trips.
The same goes for highly pointed shoes. A little point is fine, but the hard points (a la Jimmy Choo) can only be worn for so long.
For longer walking, consider thicker heels: booties, espadrilles, wedge heels, etc. At least 3/4 inch in diameter. These will make it so much easier to balance. For thicker heels that aren't booties or espadrilles, make sure they're higher than 2.5" (as to avoid the Old Lady Look).
When starting out, I'd avoid any heels that have cut outs, open toes, straps, etc. This is going to mess with your balance and possibly shift your feet around, causing more pain. You want a solid heel that curves around all parts of your foot. I'd also avoid any platform shoes (the thick line around the sole of the foot), as the weight will affect your balance.
Buy those thin liner socks, or even the 'half foot' socks if you can. This will stop any rubbing from occurring; otherwise your feet are just going to go through hell while you break in your shoes. THAT BEING SAID, the occasional blister or bump is going to happen. Heels will never be like a pair of sneakers.
If you get bruising on your toe, or lines on top of your feet or achilles heel that show the show the shoe 'digging into' the skin, it means the shoes do not fit. Try a half size larger. Likewise, if your heel shifts when you walk, it's too big for you.
The Wobble Test. Wobbling a little bit as you adjust to a new heel is normal; if you've worn the shoe more than 4x and still wobble, something is wrong with the balance (or it's simply too high for you). These shoes can be kept as Occasion Shoes, but they're not going to be an everyday heel.
Make sure the arch of the shoe is actually in the arch of your foot. I've had to walk away from many a fine heel because the arch didn't sit in the right place; I'd often feel the arch a little too far forward in my foot, which is terrible for your posture. A proper arch is key (if your arch is off on all shoes, you may need to buy a special insert).
If possible, avoid cheap shoes. I'm not saying every shoe has to be designer (mine definitely aren't), but shoe brands like Call It Spring Shoes (in Canada), or any kind of 'plasticky' heel is going to hurt. I'd say a good range is around $80-$130, with breathable, somewhat flexible material.
Practice. Practice, practice, practice! I used to barely make it an afternoon wearing 2 inch boots. Now I wear 3 inch booties or wedges everywhere, all day, 20k steps a day, and I'm fine. My feet kill if I wear flats! It's all about your feet adjusting to what you're wearing.