There are different definitions of 'units'.
e.g. one UK unit = 10ml of ethanol
one Irish unit=12ml of ethanol (10g)
one US unit~17.7 ml of ethanol
one Finnish unit ~ 25ml of ethanol
Personally I think the UK version is the easiest to work with.
Take your favourite tipple and find the percent alcohol - white wine will typically be 11-13%, lets say 12%. There are, therefore, 12 units per litre of this wine. A standard bottle is 3/4 of a litre, so that would be 9 units.
In this part of a world, for example a standard bottle of spirits (whiskey, vodka etc) is 40% alcohol and 700ml bottles, so a bottle is 28 units. Beer is 4.3% so a standard can (330ml) is about 1.4 units. A large can (500ml) is 2.1 or so. A pint (568ml) is about 2.5 units
For me, at least, there are only 4 or 5 different types of drinking scenario - e.g. a glass of whiskey, a pint/can of beer, a glass of wine etc. You fairly quickly get used to (roughly) estimating what fraction that measure is of a bottle based on experience - e.g. how many glasses did I have before I finished that bottle of wine etc, and once you've done that and the above calculation once or twice it becomes fairly easy to track (assuming you're not too drunk to remember

) how many units you've had.
Which units you've used isn't that important - just know the (safe) target levels and keep the trend going downwards towards that target (or beyond!)