I'm using the Ansmann POWERline 4 as example, but most of this is applicable to any switch mode power supply repair. I promised to make checking the rectifier bridge my new first step in case of blown fuse, that much is true. However, there's one thing even more important than that. I'm sure you're all tired of safety warnings/disclaimers by now, but considering there's no telling who are reading this, it should be stressed repair of line/mains voltage equipment should only be attempted by trained professionals.
If you nevertheless decide to try it, be aware that even when disconnected from mains or protected by ground fault circuit, the mains capacitor in even a small switch mode power supply can hold enough juice to potentially kick your heat into ventricular fibrillation. In such a case there's 4 minutes of time to begin CPR or defibrillate before permant brain damage and eventual death begins to occur. So, either make sure there is someone trained and ready to perform CPR at hand, or avoid getting shocked in the first place (Better yet, both).
To this end, be aware of the danger already when opening the case of a mains appliance, using only a well insulated screwdriver, or better yet a plastic edge with finger-guards to pry open the tabs holding the case together. Using a plastic wedge will also minimize damage to the case. In this charger, as can be seen in some of the pictures, the tabs holding it together are at the ends of the case, though sufficiently strong twist along the long sides will crack it open just as well. Working from the low-voltage "bottom" side will be safest and avoid accidentally pulling the wires from the circuit to the plug off.
After the case is open and carefully laid off the the side. Careful as the wires will wear down from tugging and bending; if you end up doing more work on the circuit board, it will save you some grief to de-solder the wires from the circuit board once you've ensured the capacitor is empty, then re-solder them the same way around after your work is done. Having to re-solder frazzled wire-ends or worse yet fix the connections on the plug end will be a pain, and cause unnecessary risks.
Next use the insulated screwdriver, a wooden chopstick or what you have to lift the green insulating paper off the back of the circuit board and tape it out of the way. Use a multimeter to measure the capacitor to make sure it's empty. In this case the capacitor is on the as-of-yet hidden flip side of the circuit board, so if you can't without a shadow of doubt locate the capacitor's leads, measure over the + and - side of the rectifier bridge which should be connected to the capacitor. After measuring it empty, make it double-sure by shorting the leads of the capacitor with the insulated screwdriver (ONLY if the capacitor measures empty, otherwise damage to equipment may occur).
The generic switch mode power supply FAQ presents many useful tips, including what to do if the capacitor is still holding a charge. NEVER work on the circuit before you've conclusively measured any big capacitors as empty AND double-checked by shorting them.
We still aren't getting to the actual rectifier bridge. If the fuse is still intact, then some less catastrophic failure has occurred. So I would (and did) check the fuse first. If the device is completely dead with no sounds or lights when it was plugged in, you have a good reason to expect the fuse to be blown. As noted in the pictures, this miniature fuse can apparently be screwed open, but that may affect its integrity, so better just measure across the logs.
A fuse is designed to completely cut off the power in case of a short/overload, so once you've identified the fuse it's a simple matter of measuring continuity over its legs. It should either conduct or not. If it doesn't, then there's been some reason for the failure, and you should seek to repair that failure before changing the fuse and re-trying, or you'll just blow another fuse.
The rectifier bridge is a similarly simple component in function, except it's made out of diodes. As the intent is to prevent reverse polarity voltage, conducting in reverse or not conducting in the expected direction should be sure signs of failure even in-circuit. Defining "reverse direction" requires the usual mental gymnastics. The leg marked with + is where the positive leg of the mains cap will rest, so this marking means "positive voltage will not pass back from this leg".
Thus, with positive lead of multimeter at + marked leg, neither mains leg should conduct to it, and with negative lead at it both mains legs should conduct to it. With negative lead at - marked leg neither should conduct, and with positive lead at - again both need to conduct. With positive lead at - and negative at + it will also conduct, but with positive at + and negative at - it won't conduct, or otherwise the cap would be constantly shorted. The mains legs do not conduct to each other, again otherwise it'd blow fuse instantly.
The diode forward voltage drop across each conducting path was just below 600mV for me on the replacement rectifier bridge, it can slightly vary depending on chip, but should be about same for each path (Except for - to + pin, as those have 2x2 diodes between them). There may be some transient readings from the caps, but they should even out quickly.
Finding out if the TOPSwitch II on an Ansmann charger (or similar) needs replacement can be tricky; the suggested test bench for determining if it works isn't readily available, and there doesn't seem to be any sources on simple checks that could be performed. However, Googling up on other repairs indicates when the capacitors go bad, the TOPSwitchII IC almost always needs replacement as well.
Since I do happen to have intact and one broken TOPSwitch II IC, though, I can tell that for my intact TOP223Y off-circuit the following holds: From source (positive, middle leg/plate when facing the printing on the component) to control (left leg) is 530 millivolts diode voltage drop, and from source to drain (right leg) is 520 millivolts. All other combinations are blocked on normal multimeter in diode test mode. The exact values will of course depend on calibration of the multimeter and this being an IC, possibly on its revision.
For the IC removed from the blown power supply, source to control is 49 millivolts voltage drop and 26 ohm resistance in both directions, and blocked every other way. The new IC exhibits no resistance. Presumably the multimeter is reading on the body diode of a MOSFET (which conducts in the opposite direction from normal current flow) on both legs, so reading no connection, resistance, let alone conduction in reverse direction of the diode should be pretty surefire way to detect a blown IC.
The other components on the board will, however, render in-circuit measurements dubious, so the IC needs to be isolated first in any case, at which point it may be easier to just replace it. Especially if everything else on board checks out, but it still won't work. With the replaced components (diodes and elco's blocking) the chip does measure as described for me even in-circuit, but with different multimeters and possibly damaged components this isn't certain.