Do your homework.
Always find out the best person to contact beforehand and send your email to them, not a general studio address. Be friendly and polite. Check for spelling, typos, double spaces or weird formatting.
Try to show how what you do fits with the studio you’re approaching.
You obviously want to talk about your skills and approach, but try and do it in a way that demonstrates an understanding of their work and what you could add to their studio. Talk about their work and find parallels with the way you approach your own work. The easier you make it for them to imagine you as part of their team the better.
Don’t ask for a job
It’s fine to say you’re looking for work, but unless the studio is advertising it’s better not to ask outright for a job – it makes you too easy to dismiss if they’re not currently looking for designers. Asking to show a portfolio is much less of a demand and people are much more likely to agree.
Send a pdf portfolio
Send a short pdf portfolio rather than a web link, with some edited highlights from your portfolio - don’t show everything at this stage because you want to keep some stuff to show them when you see them. 3–5 projects, with a little bit of text about each. Ideally no more than 10mb, but definitely no more than 20. It’s fine to have a web link to your full portfolio too, but I’m personally much more likely to click a pdf straight away, but leave a link until later (and possibly forget).
Keep your CV relevant
Personally, I can take or leave CVs, but if you are sending one keep it clear and highlight the relevant info - if you’ve interned at Pentagram or won a D&AD award, you probably want people to read that before your GCSE results.
Ask for any adjustments to the process you need
If you have any additional needs that affect how you’re able to present your portfolio, you should mention them here. If the studio’s unwilling to make reasonable adjustments to accommodate these, that’s a big red flag.