Every area is different, though, so you can start by looking up your last frost date. Around here, it's usually mid-May, which means we are almost there. Looking back at my gardening journal from last year, however, we had a couple nights of frost during the last week of May. So the important thing to remember is anything can happen when it comes to weather (Mother Nature obviously does not read the Farmer's Almanac!).
The National Climatic Data Center has a handy reference tool that tells you not only the predicted last frost date for your area, but the probability that it will be within a certain date range. Our range here is from April 22-May 30.
It's normal to want to get an early start when it comes to gardening. After all, we've been stuck inside all winter, and are craving those gorgeous, sweet fresh fruits and veggies that only summer's sunshine can bring. The first thing to consider is whether or not you are willing to go out to your garden every night, if necessary, and cover any tender crops. And I mean every night- if the weather dictates. You cannot snooze on even one night of frost if you've put a frost-tender crop in the ground, or all of your efforts will be for naught. It is a hard lesson to learn- and trust me, we've done it- to lose a plant in one night that you've been doting over inside for a month or more.
Around here, there is no longer much danger for frost-tolerant crops like onion, garlic, and peas. It is most likely safe also for the cold-hardy crops like broccoli, cauliflower, brussels sprouts, spinach, some lettuces, mustard greens, chard, carrots, beets, and the like. I say most likely because if we were to get, say, a freak snowstorm, they might not make it. But a crisp evening dipping into the thirties should be no problem.
Most of the rest of your veggies must either wait to go in the ground, or have some sturdy protection, like a cold frame. We even use gallon milk jugs with the bottom cut off, and set those over tender crops each night this time of year. But you can't forget to take them off during the day, or your plants will sizzle! The idea is to provide a barrier between the outside air and your plant that will keep it even just a few degrees warmer inside than out, to keep your baby above the critical temp.
We haven't put any of our warm-weather crops in yet, like tomatoes, peppers, eggplant, beans, cucumbers, and squash, but we will be starting next week. And we will have all the gallon milk jugs, floating row covers, and cold frames ready for any cold spell that still comes (and I'm sure there will still be frost, most certainly!). It would be garden suicide to attempt these crops without necessary arrangements.... The critical temp at which we start to get concerned for these crops is about 43 degrees F. We have had our greenhouse dip that low without killing any of our plants. But I can tell they didn't like it, especially the peppers, so I would suggest not even allowing warm-weather plants to be in air quite that chilly. If at all possible, they will be most happy if they can stay in the 50s.
Finally, don't forget to harden-off your plants before setting them out into the garden if they've been growing inside. This means setting them out during the day, but bringing them in at night for at least a week to allow them to get used to the chillier air outside. When hardening off, let the plants stay out a bit in the evening as the air gets chillier. Leave them out a little longer each day, but bring them in as soon as the temps dip into the 40s. After a week of this, they should be ready for the outside world!