For extraction from animal tissues, Qiagen DNEasy extraction kit. You'll need distilled water and 100% EtOH. As far as making sure that you maintain a completely clean environment for extraction (to minimize any chance of sample contamination) requires some experience doing DNA extraction. Previous responses that suggest visiting a lab that does this work are great suggestions.
For the actual PCR amplification after DNA extraction, protocols vary but generally follow what you see published in the main literature about barcoding. Different Taq polymerases and reagents will have subtle differences in quantities added to the 25 microliter PCR reaction. Contact me directly and I can give you some general guidelines.
Most importantly: primer choice. If you are barcoding, look and see what primers have been published within the taxa (or closely related taxa) that have been used. The sequences of those primers should be easy to find in the primary literature. There are also standard primers for animals, particularly the Fulton et al. (1994) (LCO-1490) and Breton et al. (2006) (HCO-700me) primers.
Folmer, O., Black, M., Hoeh, W.R., Lutz, R. & Vrijenhoek, R. 1994. DNA primers for amplification of mitochondrial cytochrome c oxidase subunit I from diverse metazoan invertebrates. Mol. Mar. Biol. Biotechnol. 3: 294–299.
Mr Patrick thanks for your kind words and suggestions..I am going to start Govt of India sponsored project on DNA Barcoding of Pyrlaoidea (moths) of Sukhna Wildlife Sanctuary, Chandigarh.. I had training in DNA Barcoding..for small budget I wish to skip kits..but this will need lots of chemicals and also skills..trying to be on track..hope you will give more crisp suggestions..wish we remain connected..rather i need your expert advices
Gerry Blagoev at the University of Guelph has published many papers using barcoding primers specifically derived from lepidopterans, so a search for his work should provide you with excellent references and protocols for barcoding PCR reactions.
If you working on Vertebrate (for example fish) there are many kit for DNA extraction that provide an efficient quantitative of genomic DNA such as the DNeasy extraction kit (Qiagen). I'm working on DNA Barcoding of Teleosts and If you want I can provide some of my recent paper on this topic.