First of all, load the Extractor or Sequencer with empty Storage Discs. After that, put in the organic material. Soft/Plant/Tree Tissue samples go in the DNA Sequencer, and Amber goes in the DNA Extractor (along with the raw meat of previously cloned extinct animals, if you happen to already have some).
On average, Amber gives higher quality DNA than Soft Tissue, Plant Tissue or Tree Tissue. If the DNA sequence is incomplete, it is recommended that you improve it with the DNA Combinator-Hybridizer.