The best way to weed a garden is to remove weeds when they are small, and remove them frequently--daily, if possible. Sometimes, however, you must be away from your garden for extended periods because of travel, illness, or other interruptions. Finally you are able to go back to the garden--and discover a jungle. Here's how to get your garden back.
Make it easy on yourself. Make sure the bed is moist, either from recent rainfall or from supplemental irrigation. Set aside a couple of hours so you can go at a relaxed pace, and avoid the hottest part of the day. If the location is in shade for part of the day, try to weed then. It will be easier on you and the plants.
Equip yourself properly. You'll be going after some really big weeds, and a little hand cultivator just won't cut it. Make sure you have a garden fork and a serious trowel, as well as leather gloves for the prickly weeds. Slather yourself with sunblock, wear a hat, and bring a drink.
Pace the work. Be realistic. You're probably not going to get it all done in one day, but you want it to look better than when you started, right? It is better to go after one particular weed, or one type of weed, throughout the whole bed, than it is to focus on one square foot and get every single weed.
Scan the bed. Which weeds are already past blooming, and are going to seed? Get them first. Push your garden fork straight down at the base of the weed, and pry it up. Now grab it below the crown, and see if you can get all of it.
After you've gotten all the seeders, go after the big weeds that are currently blooming. "Big" is the key concept here. You will be amazed at how much better your bed will look after all the space hogs are gone. Now go after the things trying to set up permanent residence, such as: tree and shrub seedlings (save if you want to plant them somewhere else), brambles, poison ivy, and anything else you know to be really invasive.
Now, stand back and take a look. It does look better, doesn't it? But it's not done by a long shot, right? Get a drink, stretch, and rake up and haul away everything you've yanked so far. Water any plant that had to be seriously disturbed, especially if rain isn't in the forecast.
At this point you shift from the big picture, to individual crops or plants.
Prioritize. What crop or flowers do you most want to rescue? Weed that thoroughly next, and top it off with mulch. When you've taken care of your most valued plants, mentally divide the rest of the garden into squares, and weed one square at a time. The squares should be proportional to the amount of time you have on hand, and each freshly weeded area should be mulched before weeding the next one.