You set up a campaign on a crowdfunding website, Kickstarter.com, Indiegogo.com. Those websites take care of all of the logistics of collecting payments. How they work depends on the model the particular website adheres to. Many will have you set a threshold on a minimum needed to raise in order to release the funds. If you don't make that minimum by a certain date, the funds get released back to the funders.

Campaigns usually give some incentive to fund at certain levels of funding. Usually, what people give is related to the product or service they are funding. In this way, crowdfunding is similar to the pledge drives you see on PBS stations.

Funders can rate people and comment on whether they felt the money was used properly, etc. However, you are usually not required to use the money for the purpose intended, even though you that is not particularly ethical. Doing this would also make it more difficult to fund in the future.

Some people use these websites solely for publicity for their products/services with no intention of getting any funding (if they do receive funding that is a bonus).

Hope this helps,
Jim