It is a very vast multidisciplinary field. An interesting place to start might be to check out the website of iGEM competition of MIT. There you will find the basics and many interesting projects from all over the world.
There are lots of different aspects to Synthetic Biology. I currently work on biotemplating and biomineralisation (http://onlinelibrary.wiley.com/doi/10.1002/chem.201300721/abstract or http://pubs.rsc.org/en/content/articlelanding/2012/jm/c2jm31620j#!divAbstract both highlight a lot of the work in this field). Others look at self-assembly of biomolecules (e.g. DNA origami or protein origami) or mimicing cells. The wikipedia page has good links and examples that you can search for, and the EPSRC also has some information too. http://www.epsrc.ac.uk/research/ourportfolio/researchareas/Pages/synthbio.aspx. It depends what aspect of synthetic biology you are interested in. If you provide more information, it would be easier to help you.
Googling is a great start - but the number of hits grow with a doubling time faster than E. coli (!) Useful starting points are igem.org (see above)) and the BioBricks foundation (biobricks.org). You might also want to check out the group at MIT (synbio.mit.edu), who are doing some bleeding edge work on metabolic engineering.
Of course, many people look to the "guru" J. Craig Venter. His research centre (jcvi.org) produced the first synthetic self-replicating bacterial cell, which sparked a huge number of public debates (youtube search...!) concerning ethics and future capabilities.
“Synthetic biology is an emerging research area that focuses on the design and fabrication of biological organisms/systems that do not already exist in the natural world or the re-design and fabrication of existing biological organisms/systems….Synthetic biology studies how to build artificial biological systems for engineering applications…Synthetic biology focuses on ways of taking parts of natural biological systems, characterizing and simplifying them, and using them as a component of a highly unnatural, engineered, biological system.”
i got that definition from Synthetic Biology.org how ever if you want to learn more you should try the pages listed above.. like the igem page. https://www.igem.org/Main_Page
Its really interesting you should built an igem team and i promise you will learn alot :)
ha ran into your question again... i see you are from sinaloa.. dont know anybody from there that works with synbio but in cinvestav irapuato you can contact agustino http://www.ira.cinvestav.mx/Investigaci%C3%B3n/DepartamentodeIngenier%C3%ADaGen%C3%A9tica/ProfesoresInvestigadores/DrMart%C3%ADnezAntonioAgustino/tabid/112/language/es-MX/Default.aspx :) jajaa saludos!