When one goes to a produce store or market in Israel, how does one know which stores he can buy from - that laws of trumah, ma'aser, orla, etc. have been done? Do the stores display a certificate? Are such stores listed online so that one can know in advance where to go? What about in larger "chain" supermarkets?
Shops and manufacturers have kashrut certificates, just like restaurants. And packed products also have them.
The large chain supermarkets are kosher, except for "Tiv Taam". That one exists specifically to be the "not-kosher" chain - that's what they're all about. As pointed out in a comment, there are also smaller Russian chains that operate on the same principle - they're not kosher. You can't mistake those for anything else - they have everything written in Russian, and only then in Hebrew. Smaller non-chain supermarkets, especially in Tel Aviv, as well as the convenience stores at gas stations, would, for the most part, not be kosher because they work on Sabbath, but their products would still be kosher. During Passover, non-kosher supermarkets might choose to continue selling bread, even if most of the year their products are the usual Israeli-manufactured kosher fare.
As far as produce, manufacturers in Israel are kosher - otherwise they'd lose a huge chunk of the market. So you can look for the certificate of the shop or the market stand, but there's really no need. The obvious exception is stuff that is by its very nature not kosher, such as pork.
An important exception is wine: many boutique wineries in Israel can't afford the extra pay for kashrut (the price of the certificate, ma'aser, not working on Saturday even as a visiting centre). Specialised wine shops would usually opt to carry those wines rather than have a kosher certificate. You can always ask for kosher wine recommendation in such a place.
In general, if in doubt, you can always ask. The great advantage of being in the Jewish state. :)
I'd like to add that when speaking about fruits and vegetables specifically, generally the shops will have a certificate displayed, if you can't see it ask them to point it out to you. In supermarkets (especially in Chareidi areas) each type of produce usually has a hechsher printed next to the name display. If you do end up by mistake buying produce which you are not sure about, the procedure for separating terumos and maasros is fairly straightforward. Ask your LOR (or mi yodeya!) how to do it if you end up in that situation.