Don't fill out applications online! That is a mistake. The absolute best way to get a job is to meet with the manager face to face and appear to not be a douche bag. Once you get an interview your resume no longer matters, and sometimes you can get an interview on the spot if you talk to a manager.
DO NOT make up experience. That is a retarded idea. If you apply at any corporate chain they are required to check references (all they do is call and ask if you worked there, usually they don't even ask if you were good or anything). If you have worked for any corporate chain (like Wendy's) then you can list them as a reference, since they'll have you on file. My resume is absolute shit, but I had two references so they called them, made sure I actually worked there, and moved on to the interview.
My best advice to you is this: pick up an application in store, take it home (don't fill it out in store, many managers don't like this since it seems like you aren't actually looking for the facts you need) and FILL IT OUT COMPLETELY. Like, 100%. Don't ever say "see resume" for references or anything. A resume is pretty much useless if you are trying to get hired part time at some chain. Bring back the application and resume (it should still be attached regardless of the fact that they rarely look at it) and try to give it to the most important looking person in the store. Be energetic! Managers don't want to hire people who can't even be polite and interested when dropping off their resumes.
Almost all of the interviews we grant are based on first impressions, so dress appropriately to where you're dropping off a resume and be super nice! And seriously, never make up shit on a resume. You can embellish things, but if an employer calls one person to see if you actually worked there and you didn't they will immediately file your application under the "do not hire" heading.
You can make up your availability and then change it, although employers hate this so be prepared to never get promoted. It will help you get your foot in the door, though. As for suggestions for where to actually apply: look for any places that have high turnaround rates for employees. Some stores hire people and they stay with them for a long time, which means jobs are not usually available. Some stores, however (especially stores that tend to hire younger people) might have an opening due to people leaving en masse for school or whatever. If you catch them at the right time they'll be desperate for people. Also, try to find availability where most other people don't have any (like during the middle of the day, if you take night classes). Everyone can work on the weekends and evenings, so aim for weekdays. Employers will sometimes hire people just to fill in gaps in their schedule.
edit: also make sure you are SUPER PATIENT when it comes to dropping off resumes. Never interrupt someone helping a customer/on the phone/et cetera to drop off your resume. Wait patiently.
The other day a guy interrupted my manager (who was ringing someone through at the time) and asked him "See here where it says 'have you ever been convicted of a crime'? Well, I haven't been YET, but I will be convicted on Friday so do I check it or not?". This is also a bad idea.