TTV & idle over run valve:
These should both get 12v when the ignition is on, and there should be an audiable 'click' from the engine bay when the key is turned.

3/4 Point Unit:
When engine is off, should be extended to 14.5mm. When engine is started should retract to about 8.5mm after a varying delay, depending on temperature.

Pull Down Unit:
When engine is running, you should be able to close the choke flab by hand easily until the last 5mm or travel, then resistance should be felt. If not the pulldown unit is defective or incorrectly adjusted (it has a small screw on the end of the plastic lever, but this should not need to be adjusted)

Inlet manifold preheater:
Located at the bottom of the inlet manifold, looks like a hedgehog. The electrical connection is at the back of the engine bay behind the carb, should get 12v when engine is cold, should switch off when engine has warmed up. (controlled by grey temperature sender, see below)

Vacumm Unit Stage 2:
This opens the second throttle butterfly when you have your foot down, not had a problem with this myself but I imagine sympoms for a failed unit would be no power under full throttle.

Waxstat, also known as 'Expansion Element':
Helps control the idle untill the autochoke switches off completely. Is full of wax which is heated by coolant. As the wax expands a pin exends from the unit pressing a lever which brings the idle down. Check by throwing into a bowl of hot water, the pin should extend. This has been known to fix dodgy units as it 'resets' the wax apparently!

Should get 12v with the ignition on & engine is cold, should switch off when the engine is up to temp. (controlled by the red sender, see below)
The autochoke should pass current, test by placing one prong of a multimeter on the plug, and the other on the autochoke housing.
You can check the autochoke heater visually by removing it and checking the heater spring around the outside of the unit, looks like the kind of spring you find in a ball point pen. When refitting, align the mark on the housing with the notch on the choke.

Temperature Senders:
At the front of the engine block there are 2 temperature senders, red & grey. The red sender controlls the autochoke, the grey controls the inlet manifold preheater. When the engine is cold these should pass current, when the engine has warmed up they should stop passing current. You can test units from the scrap yard by putting them in a tray filled with boiling water (just immerse the metal bit at the bottom!) to make sure they switch off correctly.

Last but by no means least, the inlet manifold coolant channel o'ring, the o'ring degrades over time eventually blocking the coolant channel completely. Often overlooked this is key to having a 2e2 carb that actually works! If this coolant channel is blocked expect poor running when cold, smoking, petrol smells, engine overruns and having the engine rev up to 1.5k+ at random until the engine is VERY hot.

Before you start, MAKE SURE you can reach ALL 6 bolts on the inlet, the third one from the right is wedged between the inlet and exhaust manifolds and is tricky to get to. You'll need a new gasket and the o'ring, part 32 in the diagram below.

First take the carb off:
Remove the airbox
Remove the fuel line from the carb
unplug the 2 electrical bits on the left side at the back
remove the earth connection from the front
Unplug the vacuum connection to the green reservoir
Remove the coolant connection to the inlet manifold
Remove 3 securing bolts
Check the condition of all the vacuum pipes, do one at a time its a bit complex back there

That should give you enough slack to move the carb over to the right out the way, next get the manifold off:
Undo all 6 bolts, remove manifold.

Then lever out the knackered old oring and clean up the hole it came out of. While you're here check the inlet manifold preheater. Then fit the new gasket & oring, refitting is the reverse of removal?

Edit: Whilst you're there you might want to replace the core plugs that are only accessible when manifold is off.