If you have the board in your hand, it's too late.
Even before or without simulation, you will have prototyped the riskiest parts of the circuit and know how they work and what to test. The less risky parts are less risky because you already know how to test them.
Therefore you already have a test plan that enables you to test that the board matches the prototype / your design intent / the simulation.
As part of the test plan you have placed a test point on every net on the PCB (or at least, every net that doesn't have a pluggable connector if you're trying to save money at the expense of more test time to plug in all the connectors. A good PCB fab house may ask for this as part of their process anyway.
Then, while the board was away being assembled, you set up a test fixture (like a "bed of nails" with Pogo pins connecting to those test points. This gives you access to every net on the PCB to test it. (Alternative : a generally rather expensive "flying probe" tester.)
This allows two levels of testing :
- With power off : that every component is correctly fitted, there are no short circuits on the board. Testing some components may be difficult because of other components fitted to the same nets affecting the impedance measurements.
- With power on : functional testing, beginning with voltage and current checks, then (for a MCU) clock frequency and amplitude, then the ability to upload test programs e.g. to exercise each pin and peripheral, then the actual app code.
Here's a very simple bed of nails fixture for functional testing and ISP (In System Programming). For such a small PCB I do the first level testing by inspection (except for PSU short circuit which can be done on the bed of nails)
If you have the board in your hand, you'll be soldering little loops of wire to various device pins so you can attach scope probes or DVM leads without slipping and blowing things up. (Yes I have done this too)