Consider what you're looking for
Firstly, consider what type of role you're looking for. What's on your wish list - what is important to you, and what isn't. What is a non-negotiable? This will help you to refine your search and ensure your values and objectives align with that of the firm. For example:
Have a think about what is important to you in a grad role - e.g. mentoring, remuneration, training and development opportunities.
Research, Research, Research
Once you have considered the above, get researching. Use Google, chat to peers and use your careers resources at University. Attend University Careers Expos and talk to firm representatives. You don't have to be in your final year to do this - in fact, the earlier you can start thinking about this the better.
Once you have your refined list of preferred firms, start learning more about them. Use your research and tailor your application for each of these firms.
Application Content
While you may have written a great generic covering letter, you need to tailor it to suit the firm - tie in your interests into their practice areas; if corporate responsibility is important to you, highlight what initiatives the firm engages in that you're passionate about. Don't forget to update the addressee at the top of the covering letter - there is nothing worse than submitting an application addressed to a different business. Oh, and proof reading is a must!
Make sure you include everything that the advertisement is asking for. If it asks for a transcript, make sure it is included. Unless it says otherwise, you can combine your covering letter, CV and transcript into one document to make sure nothing gets lost in transit. If there are multiple locations or departments, make sure you have highlighted what location and department you're apply for. Businesses often receive hundreds of applications - if they have a query about what team you're applying for, they may not always have time to reach out to clarify.
Add in all relevant work history to your CV. If you have completed internship or summer clerkships that's fantastic, but if not there may be other areas that are still relevant. For example, a shift supervisor at a local swimming pool could highlight the leadership qualities that were required in the role; or a quality control officer could highlight high attention to detail, etc. And if you have been involved in volunteering initiatives, include this too!
Good luck!