what is the best way to do a freelancing job over the summer for a student?

I am a full time student, studying in the UK with UK address. I would like to do a one time job for a company based in the USA. It will last about one month, and is mostly about creating a video animation and providing it over FTP. The value of the job is cca. 2000 GBP.

Can you explain to me what would be the best way for me to do this job? I don't understand if I would need to create some kind of business to do this, or I can do it just as a "person".

I don't plan on having other jobs soon, as I can only afford to do jobs in the summer. So this will be a one time only thing. I don't think its worth creating a company for it.

How does student internships work? I know companies don't have to pay tax for student internships. But is it because some kind of support to students, or it is just because students are not using their personal allowance? I have not used any of my personal allowance and this job would be far less then the personal allowance currently in the UK.

How can I get the most money out of this job?

I've had a similar experience in Canada.

Here I was able to work self-employed at any profession and earn up to $15,000 in a year before having to charge customers taxes.

As others have mentioned just keep good records of your incoming money and claim it as income on your taxes.

As a student I don't think you will need to pay tax however you will need to register as self employed. This is a simple phonecall to the inland revenue who will send you the information you need. You will have an extra national insurance contribution but it is small. Even as a non student your first 5k or so, is non taxable. If you did have to pay tax, you would want to make sure you have copies of receipts for work expenses as you are taxed on 'profit' not earning (ie after expenses)

Easiest thing to do between the US & UK is to do bank wire transfers for money.

I'm not familiar with UK tax laws but in the US all you would need to do is make sure to claim it on your taxes at the end of the year.

That's the minimum and easiest.

People create a company if they plan to do work for many clients, or want to protect themselves more from potential liability. If you are working on stuff where you may get sued then it helps to try and separate you personally from your business entity.

freelancers do not need a company to work as. You can treat it as an extra job , and can be taxed accordingly based on your local laws,your income might not be sufficient enough to be taxed so unless you are continuing as freelancer and earning much more than this per year, you might not need to do anything except do the work and get the payment.
You will need to know how to receive money , at least should have a bank account to get the money.