One thing to recognize is that the thread might not be a standard size. Standards exist for convenience and compatibility, but a manufacturer might choose to be non-standard for any reason. Assuming it is a standard size, it should be possible to determine which size using calipers.
The pitch is relatively easy: measure the distance between crests. You may get a more accurate estimate of the pitch by measuring across multiple crests, then dividing the measurement by the number of roots crossed. For example if you measure from the first to the fifth crest 5.0mm, it crosses four roots and so the pitch is 5.0/4=1.25mm.
If you need to take pitch from an inside thread it could be helpful to take a rubbing of the thread, then measure that. A piece of paper rubbed on the inside thread might work, for example.
The diameter is a bit more difficult. You can easily measure the inside diameter of the female-threaded part (this is approximately the "minor" diameter) or the outside of the male-threaded part (approximately the "major" diameter). The "standard" size is more or less the major diameter rounded up a little bit. This can be further complicated by the fact that the outer/male thread sometimes has its crests truncated so that the part is somewhat less than the published major diameter.
It'll be helpful to consult a chart of standard sizes and make a judgement call as to whether your measurement matches a nominal/standard size.
