What are some tips for crowdfunding science off websites like PetriDish?
These funding mechanisms are in their very infancy, so I don't know if there will any "tried and true" techniques for a few months, assuming the funding model proves to work at all. That being said, it will be very similar to that on Kickstarter:


Advertise in numerous channels. People can only support you if they know about you. Getting the word out is the primary goal in the beginning.
Provide an engaging, easy-to-understand description of:


What you want to research
Why you want to research it
How humanity will benefit from your having researched it
What success will look like

(Note: This last point is often ignored, but it's crucial for the lay-audience. They may expect a particular cancer research project to end with a cancer cure, whereas in reality it will end with the identification of a particular protein responsible for a particular mutation. Stating this will avoid making you as an individual and scientists as a whole from looking stupid in the eyes of the public.)

Offer a constant (strictly defined, e.g. "weekly" or "biweekly") updates to backers


Regarding useful perks, I've noticed that a few of the successful drives offered things such as:


Engrave the name of the backer or a loved on the instruments being used
Paintings of the organisms/landscape/imagery being studied
Naming a star/organism after the backer/loved one


The final topic, transparency, is more difficult. On the one hand, you will need complete transparency. On the other hand, there is such a thing as too much transparency. In brief, your updates should serve to inform the backers about your work, while simultaneously and more subtly serving two other goals as well:


Convince your backers that you're actually doing work
Maintain their confidence in your ability to do the work




tl;dr - 


Make everything  - everything - about your proposed project crystal clear for the layperson
Make the prizes cutesy and attractive, but not too lavish; they're investing for science, and secondarily maybe a little gift
Your updates should, in order: (1) inform about your research, (2) convince the reader of your scienceness