I have come across a startup in the very early stages, and I'm interested in working with them. They recently posted a job opening for a web designer and I want to apply. Is there any specific thing I should do regarding applying to a startup? Like a cover letter or something else?
Better than a cover letter is to actually proactively DO something to help them. It'll show them not only that you've researched them, but you're passionate about the startup and worth bringing on.
A man got a job at Square early on for just making them a marketing video on his own (back before they had one). Since you're a web designer, design a stellar 1-pager that's targeting their message to a particular niche. Something they could use on social media or something.
If they're like most startups, they're not interested in reading cover letters. They're interested in passionate individuals who can add value to the organization.
Cover letters are for bureaucrats in government offices or companies with HR departments.
Startups may evolve into Microsofts; but, for the time being, they'll be oriented very differently. Either they'll be dreaming about future success while staring at the ceiling or else they'll be working 25 hours per day to connect the dots.
The first kind of entrepreneur might like cover letters, and that project will generate lots of mission statements, business plans, and little else. But the practical entrepreneur with a chance of success will look at a cover later impatiently and maybe throw out your application because it doesn't get to the point.
If you must write a cover letter, make it a list of the work you'll deliver and the date you'll deliver it.
I'd suggest calling them or contacting them directly and asking what they need.
In my experience (launching startups and coaching them) - owners and principals are interested in attracting passionate and talented people to joint the team.
Certainly be ready to provide them with a resume or a CV if requested. But also be ready to share with them what YOU will bring to the team and to the company to help them succeed.
Best of luck!
PICK UP THE PHONE AND CALL THEM....
Cover letter? Are you kidding me. The only people who write cover letters are "no one".
If you can find a phone number then call. If not, drive to where they are and meet with them. If you want to work for them bad enough, you'll invest the effort into talking with them face-to-face.
In all my 15 years as a founder, I never engaged an advisor based on a cover latter. So I suggest that it is waste of time. You can get much better results by doing some indept research about the prospect and their pain points, and thinking thru how you can add value with specific strategies/ideas. Think about all variables and multiple options. Then use your social and professional networks to get to meet the key decision makers. Finally make you case. If you do a good job you will get hired!