Let's give this some context. You're a pump engineer and you've been called out to a standard float-controlled wastewater pump station that's not working. The pump hasn't tripped and turning it to hand doesn't bring it on. So what's wrong?
First the safety bit: only carry out these checks if you are competent to do so, and at all times follow all of the necessary procedures to stay safe (think safe isolation, live working, etc).
In principle what we're going to do is to follow the power to find out why it's not getting to the pump. You'll need a multifunction tester for this.
Here's a simple 8-step approach. If the answer is no to any of these questions then that component is the faulty one. Remember that the problem is often loose cables, so check for that before replacing the component itself.
Do a visual check. Are the breakers all on, is there any sign of damage, are all the cables connected? And while we're assuming that the pumps haven't tripped, just double check that on the overload itself, in case the trip lamp has failed.
Check the incoming power. Do you have the correct voltage? If it's a 3-phase panel check the voltage between each pair of phases as well.
Make sure the isolator is working - is the voltage present on the outgoing isolator terminals (when it's turned on)?
Then follow the mains power to the MCBs, down to the contactor incoming side, then the contactor outgoing side, then the terminals on the din rail. Have you got voltage at each point? You'll need to make sure the contactor is enabled/energised for the power to be coming out of the outgoing terminals, if the contactor doesn't come on with the switch turned to hand then on to the next point...
Now to look at the power on the internal controls circuit. Do you have power on both the primary and secondary side of the transformer? On the secondary side check between live and neutral, rather than between live and earth. Sometimes there may be a DC controls circuit, make sure your multifunction tester is set to DC voltage if that's the case.
With the switch turned to hand do you get the correct voltage between the A1 and A2 terminals on the contactor? Check this on both contactors if it's a dual pump panel.
Ideally now follow the controls circuit through from the transformer to the contactor. This will likely go through a stepping relay, a hand/off/auto switch, an overload's auxiliary terminals, a pair of klixon terminals and maybe a relay or two. Does it follow through everywhere it should go right down to the contactor?
By now you should have identified the issue. Either there's a problem with mains power, or the contactor isn't allowing power through it due to a fault with the controls circuit of the contactor itself. In some cases you can bypass the fault temporarily (as long as it's not a safety device such as an MCB) to get the pump up and running, as long as you don't leave it on hand to run dry.
Here's a bonus tip - one of the most likely things to fail is the stepping relay. They are the cause of many failures on pump panels, there will often be a mark on the side showing they have burnt out. However there is a new type of stepping relay called the Universal Relay which doesn't have this problem, more information here: www.gandgcontrols.co.uk/post/why-do-stepping-relays-fail-on-pump-control-panels