My daughter just turned two, and over the last two years, I've learned a lot. Most parenting skills were easy to learn, but I never figured out burping when she was in the infant stage. In retrospect, I think if I had tried to burp her more often, she would have been more happy (with less crying). For future reference, when do you need to start burping, and when can you stop?
Both my sons needed to be fed by bottle early on (my wife didn't produce enough to breast-feed). What we experienced was that if we didn't take a pause to burp in the middle of the meal, he would more likely gulp up when finished. So for us it was basically twice for each meal (one in the middle of the meal, and one after finished). It was not always easy to "produce" a burp, but it was worth it. We often saw that when we couldn't get a burp for some reason, it was likely that he would get some stomache ake later.
With my son, we burped once in the middle and once at the end of the bottle and, with the exception of maybe once or twice, that was generally plenty. By the time he was 7 months old, though, we could back it down to once at the end of the feeding unless he slowed down and seemed to indicate that he needed to burp.
With my daughter, who had reflux, it could sometimes be as often as at the end of every ounce if her reflux was especially active that day. She is an exception, however, not the rule.
Ours were breast-fed, but I got to feed them a bottle as the last feed before night-time sleep. They all needed a burp after that bottle.
Generally they got the whole thing down before needing a burp, however occasionally they would slow right down before finishing, and invariably a burp was all that was needed before finishing off the bottle.
My experience is that if my wife breastfeeds, my daughter has very little gas. She may need to be burped when switching sides. The bottle gives my daughter more gas. I burp her a few times every feeding. If she gets squirmy, that's her telling me that something is uncomfortable. But each child may exhibit different signs.
With my daughter, I burp at the end of every bottle, or if she starts becoming fussy at the nipple I'll burp her then too (to make room for more). She tends to drift off when she's sated, so if she's fussy she's either in gas distress of some sort or we've been trying WAY too hard to get her to take a bottle she doesn't want.
When burping, I'll generally use a flat open palm with curled fingers (providing a relatively flat, not-floppy surface) and pat firmly about twice to three times a second. If a few minutes of this does not result in a pretty audible belch, she didn't suck much air when she was feeding (certain bottles are better at this than others; we've generally had good results with the Playtex VentAire series. It's all about nipple shape, proper flow for your baby's age, and preventing air mixing with formula as the pressure in the bottle normalizes) and I don't worry much about her not burping.
Sometimes, I will also leave her in a reclined position after feeding for a few minutes. Not enough time for bubbles to enter the intestines and become gas, but enough time for the bubbles to consolidate towards the top of the stomach. This generally reduces spit-up in my experience, while giving that satisfying belch that lets me know she's got it out of her system.
For the record, both our midwife and paediatric told us to put the baby on the breast, facing us after each meal. We should gently pat her on the back a couple of times. We should not wait for her to burp but pat her a only couple of times. Our daughter usually burped very quickly, but the advice was specifically not to try too hard to get a burp; if she needed, she would burp.