What are some business ideas that will cost me close to nothing?
I'm a student looking at various options
Nothing costs nothing, but in your position you have time and so investing your time is the cost of any endeavour you pursuit. They the question becomes what can I spend my time on which will get the result I want.
It is worth considering what you're goals are to, might be money or passion or something else.
But onto your question:
Business ideas that cost basically nothing is working out something you are able to do that other's find valuable, it could be literally anything - start writing about it, talking to others in similar areas, find a way to engage with people that have the money (probably not other students) and are willing to pay for your ideas (information) and/or ability to do something for them (service).
These types of businesses are super low cost to start, you could start something basically fully on facebook and then expand when you are making money.
I've also heard a great strategy for starting something new, it was to focus on something high value and high cost initially, this will give you the capital to continue to grow the business and develop other areas of your business that might be low cost/low value but mass market and recurring revenue. High value and high cost generally is some form of consulting.
Best of luck, nothings - easy even with money - so stick it out and make it work.