As people already mentioned, you have several options:
1. Use timegrapher. Most watchmakers I visited use them, I heard that they are fast, accurate and pretty easy to use. Problem with them is that you have to invest money to buy one. If you are not seriously into watches I suggest moving on with the list.
2. Use some application on your mobile phone. There are numerous apps for this purpose, both for iOS and Android. They should be easy to use, some of them are free and some are freemium (so I've heard).
3. Use simple spreadsheet.
I'll try to elaborate method 3 because I use this every day.
First, you find some online atomic clock that you are going to use for comparison. It is very important that you compare your watch with (the same) atomic clock every time. Don't use other watches/clocks because they are not accurate and most of them have some daily deviations. Make the first reading, compare your watch with atomic clock (ie. if your watch has second hand wait for this hand to be in 0 position and note the time on the watch and atomic clock). You will have your first reading - note the time difference between the watch and the clock. (let's say your watch is 5 sec late). After some time (for the sake of argument, let's say after 24 hrs) you repeat the procedure. You'll get another reading (let's say your watch is now 10 sec late). Judging by those two readings, your watch lost 5 sec in 24 hrs.
If you do this often you'll notice that your watch gains/loses time differently in different positions (face up, face down, crown up, crown down etc.). Naturaly, it will bahave differently while it's on your hand. Force in the spring has influence on the accuracy also. Other factors also influence time keeping (temperature, pressure, magnetism etc.) but that's another, very complex and interesting subject. Hope this helped.