This is really going to depend on the company. Generally earlier stage startups can be more flexible with the equity they can offer. More established companies are going to have limits on what they can offer so there will be less room to negotiate.
I think first you need to try to work out what the approximate value of the company is and what it could be worth if all goes well -- if the company has recently raised money this would be the best way to gauge the current valuation.
If equity isn't already being offered, ask for it, perhaps in exchange for a slight a reduction in salary. If they offer you 1% and you know the current valuation of the company you know exactly what they're offering which will allow you to better assess whether that's a reasonable offer and also if it's worth making a counter offer.
The only experience I can share is that I personally don't believe it's worth asking for stock options in exchange for salary in the majority of cases. Remember, most startups fail and if they fail you're effectively receiving nothing in exchange for a reduced salary. Even if this is a larger more established company then you could always just take the extra salary and invest it in the public market in similar companies -- perhaps ones you like more.
If you really believe in the success of this particular company then go for it, but after a decade of personally being screwed over and watching friends similarly get screwed over, I promise you the dream of making bank in a few years on stock options generally doesn't play out. In fact, I'd personally recommend asking for the opposite whenever stock options are offered -- a higher salary without the stock options. If you're making $5,000 - $10,000 more per year and investing that over 5-10 years 99% of the time your personal investments will be worth more than any stock options offered.