Timing is incredibly importance when you are applying to internships (as well as Graduate programs). Many companies conduct interviews on a rolling basis instead of handling them all at the end.
This means that spots are filled as people apply and because companies (large ones at least) have certain budgets allocated for the program spots could be gone by the time you apply if you decide to apply late.
This however, does not mean that you should rush things. Make sure your resume and accompanying documents are you order (cover letter etc.). If you can get a referral for your application, even better. A well-done application with thought put into it is better than an application that is hastily done or rushed.
Your resume is your first point of contact with a recruiter (usually). This means that your resume is incredibly important.
A well-done resume should convey to a recruiter your accomplishments, achievements, and experiences. It should be easy to read and be straight to the point. Generally resumes should be 1 or 2 pages long. Anything over 2 pages is probably too long.
When I applied for internships I had a 2-page resume. Always get your resume checked by someone else. Your resume should never have any spelling mistakes.
Most companies these days do not require a cover letter. For ones that do, or do not specify, it could be a good way to convey your desire for the position and what differentiates you from other applicants.
When writing a cover letter keep it short and succinct. A paragraph structure as follows worked well for me:
Paragraph about who you are, what you are studying, why you chose your course, what position are you applying for. Paragraph about the position, the responsibilities and why you are suitable Any closing words e.g. If the company has a certain value that really speaks to you this is a good place to mention it Of course, this is not the only format. Just remember to keep it relatively short (1 page).
How to answer application questions
Know your motivations for applying to the company. When I say that I don't mean the "Because I want a job" or "Because I need a job". Understand or realise why you applied for this company instead of another. Was it their benefits? Was it because they won an award sometime back? The more you can show your reasoning for applying to the company the better chance you have.
Always try to research the company before applying. Know what they do, know what products or services they offer. Understand their values. Maybe even look up a few recent news articles about them. This will show the recruiter that you have taken the time to try and understand the company and will give them a reason to invest their own time into you.
Referrals are a good way to get your application noticed by the recruiter before others.
Referrals are when someone within the company recommends your application/resume to a recruiter. Different companies weight referrals differently, sometimes referrals can allow you skip some interview steps and sometimes they don't give you much of an advantage.