Make sure you write your resume out really well then apply apply apply. I find the hardest step is getting to the first interview, once your resume is accepted it's easy to charm the interviewer. Employers care more about experience than education so it's important to get that first entry level job then afterwards you can look for a better job if you need to. Don't come across as desperate i.e. "please I really need this job!" Instead make them think they need you more than you need them.
Before the interview, google "top 10 job interview questions" and prepare answers like you would for an exam, entry level job interviews usually have some of the same questions. To answer the questions use the STAR method- situation, task, action and results (google it). Do some basic research into the company/organisation you're applying for, it could just be something as simple as looking at their website. Then in the interview you can use this basic knowledge to show you're interested in what they do.
Also understand that if you are not accepted, it may not have anything to do with you. A lot of hiring teams/employers are incompetent. You will see some companies will have the same position advertised for months and months because they suck at hiring.