Every field note must start with date, time or time duration and the location. For some observations data on the exact location is also can be valuable. If an observation was made 100 m towards North from a known location X, the location is X and exact location is 100 m towards North from X. Apart from these data, data on weather conditions are also necessary for a field note as it affects on the environment, activities of organisms, your visibility (due to light intensity) and many other factors that can make a significant difference in your data.
After noting down these things, you can proceed in obtaining data required for your study. There are many things that are important in data gathering, but they vary from a study to study depending on the methodology. Thus it's not practical to state them all here.
Let's just see what we must note down when we need to identify an animal, as a lot of nature enthusiasts are interested in this. When we encountered an animal we can not identify, we have to note down several essential data on it. Such as size, shape, colour, habitat, micro habitat, behaviors and call if possible. In some cases we can measure the size accurately, if not make sure that you note down it comparing to a known object or an animal (length about a pen, slightly larger than a crow). For shape and colour we can make a sketch. Do not forget that a sketch is a sketch not a painting. You don't need to be an artist to draw a sketch and you really don't want to colour it. Just make sure that you draw it with correct proportions and colours can be indicated using arrows.
Both habitat and micro habitat are very important in identifying a species. Thus make sure that those data are obtained properly. For a fish a fast flowing stream can be it's habitat while bottom of the stream is it's micro habitat.
If you can observe the animal for some time, note down any data on it's behaviors. Some special behaviors can help in species identification.
Some species can be determined using one or few characters while you need different characters to identify another. (Usually colours and size is enough to identify a bird, but colour has less importance when identifying a frog) If you are sure of what to look at, you can give priority to observe that. If not, make sure that you gather as much data as possible as it'll give you a bigger chance in determining the species your looking at.