Applications are filled out electronically online. The directions are on the applications tab in LSAC's online services section. You fill out the application using Adobe Acrobat, sign the application electronically (sometimes you have to print out a signature page to mail instead), use your credit card to pay the fee, and the application gets processed and sent out by LSAC. You don't have to print or mail anything and you can see online exactly when your application is received by the school.
Each school has different personal statement prompts. Some are very different. Most are the same. Get on the websites for each school you are looking at and find last year's application if it is still available. The questions probably won't change so you can get started on your essays for them. My personal statement went to all 6 schools I applied to, with some extra optional essays here and there.
The "Why X School" essays are usually called "optional." They aren't. Informal polling around here suggests you have a MUCH better chance of getting in if you right the essay. Michigan and Penn come to mind. (Some people try to stick in a paragraph at the end of the PS about "why X school" but it's probably more effective as an entire optional essay)
Resumes are submitted through LSAC. You upload them as doc files and they turn them into PDFs.
See each school's website for last year's app for the personal statement prompts. This year's apps won't come out until September or so.
Your next step is to write your general personal statement, check out the optional essays you may need to write, and start those if you want to. Assuming the questions are the same (which they usually will be) if you can get it done by September 15th or so you'll be in good shape.
PS - You may want to go to the library and check out a book on applying to law school and writing essays and such. They have a billion there. Your questions are pretty general so a good overview of the process might be helpful.