Stick with updated copy of Standard Methods for Analysis of Water and Wastewater (book). Most water labs and perhaps libraries have copy. There are various water sampling tools and equipment, some of which depends on what specific is being sampled. If sampling a major river, a grab sample from the bank is unlikely to be representative. If you want to sample water in well from tapped aquifer, you might need to pump well before sampling to get fresh water input, and purchase or make sampler that can be opened at desired depth, filled, then closed before pulling back up. Various scientific or water quality instrument companies could be consulted for available samplers. Also you might consult with water agency, geologist, hydrogeologist or well driller for information or even help or collaboration.
Perhaps this may help. https://www.elgalabwater.com/blog/total-organic-carbon-toc
Proper sampling procedure and an appropriate sampling point should be implemented to get a representative sample. Ensuring that the water was not stagnant but free flowing, proper sample size, frequency, sampling material, reduce contamination, etc.
For total organic carbon , samples are not filtered. Filtering the sample will profile the dissolved organic in the sample.