What is the best way to try and get a referral?

I am currently on my 1 year long job search and have always struggled on reaching/connecting with people on LinkedIn so that I can get a referral. I feel weird just asking, "Hey John Doe could I ask for a referral?" What would be the best way to do that? Also would it be a good idea to apply to some jobs first then tell someone at the company you connected with that you applied or wait for them to refer you? I honestly was never given help at my University Career Center with this, so its all kinda new and a very important thing to learn and do. Any advice or help is awesome.

I am currently in the hunt for a job post college. However with the 300+ jobs I have applied to, I think I have also got that many phone calls from spammers. However, some of them are getting good. They use a CallerID (that isn't even the name or company they are) most of the calls are from stupid insurance companies. So I have started to play with them by pretending to be different food companies (PizzaHut, Papa Johns, ect.). I think this is more fun. What have your experiences been lately?

I recently joined DevRants, and with me joining any new site or media where you can share I am usually the guy who is shy and likes to sit back and watch/read. However I wanted to post a question as I am trying to get a job within the Cyber Security field. I have a computer science degree and honestly I feel like I can't even code at a level I should be able to. I am also currently working/studying for my CompTIA Security+. It has been going good but, I always second guess myself and doubt my abilities. I guess this a a slight rant and question so far.

My question is how can I better improve both my skills (coding, linux, and security) and also my mental. I would say its imposter syndrome but I don't have a job so I don't think it would be fair to say it is. I just want to break into the job field and show people that if given the help and resources I can excel at the task given. I do learn fast and pick things up pretty good. Any help/recommendations is much appreciated, and I look forward to more talks.