I'am a student and joined a Startup as a summer intern, as a Web Developer. Later on I said that I am willing to continue work for at least 1 year (part time) and they agreed. Is it okay if I ask for equity share since they are not able to pay!
And if yes, then upto what percentage can I ask for, I am working under the Technical Co-founder and will be giving at least 20 Hrs/week.
First, you should not be working for free. Not in software development when there are plenty of companies desperate to hire developers.
As to your question: they should be paying you and since they don't have cash, they should be paying you in equity.
And yes, you should ask for it. If you don't ask, you won't get.
However, you're unlikely to get it. You have weak negotiating position because you've already demonstrated you're willing to work for free.
Ask for equity and if they don't give it, quit. Find a paying job (there are plenty of well paying jobs those days) or start your own company/project or focus on building your reputation (by writing open source code, blogging on technical topics etc.).
Better yet: just quit. Equity is terrible pay because it's extremely risky. If startup fails (probability of which is 90%) it's worth nothing. If you're ok with that risk, that's fine. I wouldn't be but it's a personal decision.
As to how much equity to ask for: do the math.
Decide how much you would otherwise be paid for your 50% (20hrs/week) time. Let's say it's $40k/year.
Figure out the current valuation of the company. If the company had a funding round, use that valuation. If not, make one up. Let's say it's $1 mil.
If you were an investor in that company, $40k would give you 4% of the company. That is the absolute minimum you should ask for, but you should adjust upwards for the risk. Let's say there's 90% chance the startup would fail, the fair compensation would be much higher (too lazy to do the math, look it up, but basically it has to compensate for the fact that there's 90% chance you'll get 0 and only 10% chance that you'll get $40k i.e. 4% of $1 mil).
Now, the fact that fair compensation is much higher than $40k doesn't mean you'll get it. An investor, for example, can't use that logic. On the other hand, an investor can minimize the risk by investing in multiple companies, so if he invests in 10, there's a very high chance at least one will succeed. You don't have that luxury.
I'll repeat my advice: don't work for free. Find a paying job or start a company or build your expertise and authority. Anonymously working for free is the worst option. Even working for equity is a bad deal due to overwhelming 90% probability that this equity will be worth nothing.
I have a very simple model for deciding if a work situation is fair or not, basically there are just 2 ways you should work:
Basically, if you are not in one of those two groups (and you don't have a very good specific reason) you are taken advantage of.
So, you should either get a fair salary (unlikely since they already know you are willing to work for free) or a significant amount of equity (significant equity for a summer intern, no way) - you should probably quit (it's not really quitting because you were never really employed) and go work somewhere else for actual money.
I feel you should ask for some form of guarantee, you might never tell, they just might not have your best interest in mind. Besides, there is no harm done in you asking, afteral its not like they'll fire you or something