In many cases, it's not about what you've done but why it is significant and how you can benefit the company by applying those skills. In essence, blagging, but never lying.
Match your skills to what they want. If you research the company, or similar ones, you might be able to find a job profile. If not, speak to people you know who work in that area and try to identify the main areas they'll be assessing you on. Working in a charity shop will involve helping customers, resolving issues, conducting sales/refunds (till experience), stocking shelves (maintaining an inventory) and reporting to a manager. You may not have done all of those, but try to gain experience and just beef up what you do have.
Try to speak to the manager or ask for the person who deals with HR or another senior position. Avoid walking in and just saying "I need to speak to the manager" as you might imply you have a complaint to raise, so start your job application procedure as you enter the store. Dress smartly, be polite and explain why you're there and if there was a particular role you've seen that you want to apply for. If it's a spur of the moment and you don't know if they have a job, still just explain that you're looking to speak with the senior person regarding careers. If they tell you there and then that they have no jobs, consider asking them to keep the CV on record (they will usually tell you that's what they want to do anyway) and try not to sound disheartened and convey your interest to work there. Make them want to call you back if something comes up.
It is always worth including a covering letter to really state why that role and that company is right for you and the CV will provide more generalised supporting evidence. Say that you're looking for full and part time opportunities as this widens your scope with them. Be careful how you mention university though - some people even remove evidence of attending university if they're going for "store jobs".
If you wish to keep it on the CV, how will that job and that degree go together? Are there skills which are shared and how will you make a long career with that company if you're still at uni? Perhaps you are studying fashion or business and want to work for that store as a graduate. Maybe you're doing something completely unrelated and just need the money - In which case, tread lightly. You might be able to join a store local to university, but they'll still be considering your motivation for applying for a job, so think of an answer. They don't expect their employees to be with them for 50+ years, but they will clearly expect a moderate commitment and you won't want to give them any reason to shy away.