In Civilized Areas, They will Tell You Automatically
Today, ships and aircraft have systems that self report their name, size, exact location, velocity, destination etc. For ships, this is AIS, and for aircraft it is ADS-B. The systems automatically squawk their info aat regular intervals, so as soon as you are in receiving range you know what the contact picture is.
It is often required by the relevant authorities, as it significantly improves safety when everyone knows where everyone else is.
Otherwise, IR will give a Good Guess
All vessels will have a power source. This power source is going to have waste heat, which will radiate from the vessel evenly. (Unless the owner pumps air/fluids around to deliberately alter the heat transfer.) This waste heat will be subject to one over r squared losses. If you can determine a range, you can determine how much this blackbody radiation will have dropped off, and you can get an estimate of the size of the power source.
Power is going to be strongly related to vessel size and acceleration. The exact equation is probably going to be complex, but luckily the universe is full of vessels providing you with empirical data!