When it's been 15 days since your last quest, go to a village.
Stay in the village for a full day. Try to talk to everybody but also hang out doing some crafting (making boards or whatever) because there are some quests that only one person in the village knows about and you won't get the quest unless you talk to that one person but if you stick around long enough, they'll come up to you and start talking.
Sleep in the village and then journey on to the next village, staying a full day in that village, etc.
I think, but am not sure, that you have to enter the village from the zoomed out map by walking into it; ifyou zoom in early and walk in on the zoomed in map then I think it doesn't work (but maybe that was fixed?)
If you miss a quest in a village you could go to dozens of villages without ever finding a quest because you have to wait until that one you didn't find expires, so make sure you stay in each village long enough to be sure that you didn't miss anything.
(and sometimes it takes even longer than that; i've got a character right now who has been a whole month without finding anything and spent most of the last few weeks sleeping in villages to no avail, so there might be something else i'm missing or just might be having bad luck. But usually these tips work!