How can I convince the employer to hire me?

1.
mention your skills clearly.2.
mention examples for some situations and how you deal with it and how you solve it.3.
mention you job tasks in details.4.
try to support your responsibilities by mention an examples.5.
self confidence is very important so believe in your self and your abilities and let that clear in your actions and re-actions.

simply trust yourself, have the confident.
don't exaggerate talking about you and your skills .be honest try to focus about convinces him by your response and your attitudes ,make him feel that he are talking with a smart girl .

First of all answer the same question in your mind.
After all why should the employer hire you? after whats so special in you that one should hire you ? If you find you answer ....
be confident and believe in it.
Any employer would itself sooner or later see that confidence...
and you'll get hired.
but the main question is what IF you can't find answer to this question.
We'll in that case you need to find the areas where you think you're unbeatable :) All the best for getting hired.