It depends on the veggie, either look on the plant label or seed packet. It should tell you the specifics of the plants. Good luck w/your new garden.
Here's a good guide to know when to harvest things
Also another good site.....www.vegetablegardener.com. Very informative on veggies, how to grow and also prepare once harvested.
WOW...my question was for POTATOES...but I found out its when the plant/leaves wither and yellow...I just asked because I NEVER saw potatoe plants get as big as mine are....they are like 5 feet tall or taller....not sure how my question got murdered, but ok
Next time you grow potatoes, try "hilling" them. When the plants are getting tall, begin building up mounds of good soil almost to the top of the leaves. Potatoes grow in a chandelier pattern and the more you hill them up the more potatoes you will harvest. You can do this a few times, I did last year, then missed a few potatoes in the ground...I had a nice crop grow just from those forgotten ones.