I cannot answer for fertilisers but composts are analysed like plant samples.  Do you want colorimetry for P and AAS for metals, or ICP techniques?

There are standard procedure for estimation of different micronutrients. You may see AOAC to know methodologies

For Soil/Compost anaylsis, you can use some of the procedures with Jackson ML 1973. Soil Chemical Analysis. 

Pl find some attached links and files. I have no idea about chemical fertilizers.

http://www.imperial.ac.uk/media/imperial-college/research-centres-and-groups/environmental-and-water-resource-engineering/ecwm/phase-1/Section-3.PDF

https://archive.org/details/soilchemicalanal030843mbp

Dear Friend,

I suggest you the following book for your use:

P.K. Gupta (2013) Soil, plant, water and fertilizer analysis (2nd Edition). ISBN 9788177543063. AGROBIOS (India), AgroHouse, Chopasani Road, Jodhpur 342003, Rajasthan, India.

Dear Dr. Kamal,

As you are also interested in analysis of organic manures, I recommend yet another a more relevant book of analytical procedures for you:

METHODS OF ANALYSIS OF SOILS, PLANTS, WATERS, FERTILISERS AND ORGANIC MANURES . "2nd revised and enlarged edition (2013). Edited by Dr. HLS Tandon.  ISBN: 81-85116-55-5.  

You may contact the following publisher to get a copy of this book:

Fertiliser Development & Consultation Organisation

204-204A, Bhanot Corner, 1-2 Pamposh Enclave, New Delhi-110 048(India)

Phone/ Fax: 91-11- 41633864 

Email : [email protected]

Website : http://www.tandontech.net

Hope the information is useful to you.

Many thanks Dr. Dilip Kumar Kundu ,

With best regards

Dr. Kamal Hama Karim