How do I take 10000 readings of a waveform and then obtain lowest frequency, highest frequency, lowest period, and highest period using Agilent DSO 80204B?

First, it would help, if we knew more about your waveform.

Beyond that, there are a few solutions. If you need exactly 10000 measurements, then you will have to remotely control the scope. If the number of measurements just has to be larger than 10000, then turn on a Period and Frequency measurement, and let the scope run until you have accumulated more than 10K measurements. The stats at the bottom of the screen will tell you the largest and smallest of both measurements. If you have EZJIT, then you can capture that data much more quickly, because it will make measurements on every cycle of every capture. If the signal has a high enough frequency, and you have enough memory depth, then it might be able to do it in a single capture.

Beyond that, there are a few solutions. If you need exactly 10000 measurements, then you will have to remotely control the scope. If the number of measurements just has to be larger than 10000, then turn on a Period and Frequency measurement, and let the scope run until you have accumulated more than 10K measurements. The stats at the bottom of the screen will tell you the largest and smallest of both measurements. If you have EZJIT, then you can capture that data much more quickly, because it will make measurements on every cycle of every capture. If the signal has a high enough frequency, and you have enough memory depth, then it might be able to do it in a single capture.