As an employee, you know that sometimes you're going to have to suck it up: work through a lunch, stay an hour later, come in an hour earlier, work a night, work a weekend, shorten a vacation...every once in a while work asks extra of you, and, because you like working there or are in love with the concept of money for goods and services, you put up with it to prevent a stoppage in the flow of dirty lucre.
Typically, someone has to ask you to do that.
As the manager, boss, project manager, etc., you're the one who is going to have to ask people to do that for you.
Now, my other posts still apply, of course; if you suck at being a boss or are a lousy person, there's a good chance no one will go more than an inch out of their way for you.
But there are other things to consider when asking people to go above and beyond the normal call of duty.
For example, what will you be doing when people are working those extra hours? Will you be at home watching TV? You shouldn't be. Even if there's squat you can actually do while they're doing the heavy lifting, you should be there, where they can see you. Employees put a lot of stock in people who stick by them, especially in sucky situations and even more so in situations where you don't have to. Now, you don't have to stay the whole time, especially if people are trading in and out of the extra time. But you do have to show up, show some hardship for what you're asking them to do for you. It goes a very, very long way towards them doing a good job and being willing to do this for you again someday.
Next, how often have you asked for this special brand of favor? My preference--and we know the world doesn't revolve on preference--is not to ask people to work extra late/weekends/early more than once a month if I can help it. In the tech industry, many people are familiar with "crunch" time, when extra hours are required of everybody, but even in the tech industry, if it's not actually "crunch" time you want to think long and hard about asking for the extraordinary because if you tap that resource too often people aren't going to want to give it to you later, when you need it. Worse, they are going to start to resent you, which makes for all kinds of serious problems managing them during normal work hours.
Also, think carefully about how useful additional extra hours will be. If you've asked this favor for the last two weekends, they aren't going to be fresh on Saturday when they show; it might be worthwhile to skip working the weekend entirely, give them time to recharge, and try again later. People do burn out, and that makes for bad work that lasts longer than crunch time.
Next question: what do they get for doing this for you? A lot of people feel that, because their job includes some non-work regular hours, they should do it simply because its their job. While you might feel that way--and heck, they might, too--its too much like taking people for granted to say it. Staying late or working a weekend or coming in early or missing a lunch is unusual and extra and they don't actually have to do it, even if their contract says it, because they could always get another job where they don't have to do that (or can do it on their own terms). At the very least, you must acknowledge what they are doing for you is above and beyond, and thank them, preferably doing both regularly and publicly.
Where possible, provide incentives. Some companies will expense dinner or lunch for people working through lunch or dinner or on the weekend. You can always ask, and they can always say no, but if they say yes, you have advocated for your people. A free meal is not, by any means, equal to giving up their private time to you, but its a good place to remind them that you do appreciate them and you will go to bat for them in whatever ways you can.
No expense account? Take up a collection for pizza and donate extra to the pot for your people. Or, bring in donuts or bagels or soda or home baked goods. It doesn't have to be expensive, but it has to be a treat and a symbol of your appreciation for them.
Can you do comp days? Can you excuse them a much longer lunch (or two) later next week? There are a lot of ways to compensate people that don't require cash. Just make sure your options are legal and approved by the people who would get to use them.
Note, working a Saturday, in my opinion is not equal to getting a Thursday off. Trading days one for one is never my idea of a good time. When I can, I try to give more time for a weekend day than a weekday of work. If that's not possible for you, you can arrange those comp days in a better way for the employee...such as a four day weekend, for example. Be creative. Be thankful. Let them know.
Next, can you make the above and beyond suck less? Sometimes working just the Saturday and giving people Sunday off is way better than half of both days (or vice versa). Check in with the team and find out what floats their boat. Majority should win, though the next time you can try it the other way to please the people who didn't get their option this time.
Will there be a long period of waiting? Managing devs, they often have to wait for the testers to finish, and vice versa, or Operations has to wait for the team to finish. Bring fun stuff for down time; games, treats, toys. Look up interesting things on the web and have them available to share (but, of course, make sure they aren't anything HR will come after you for showing). APOD has these awesome star pictures, but some people are into LolCatz. Know your people. Let them laugh and have a moment as a team. It bonds them, and they work better.
Finally, reward them. They do the work, and you praise and publish their success, and you reward them. It can be as simple as bringing a board game to play over a long lunch, or hitting a restaurant as a team, or letting people go early (outside whatever comp deals you may have set up). Now, I'm not advocating letting people spend tons of time away when you do need them the most, but I am suggesting that you give them what you can when you're in crunch, and then be generous with them when they're not in crunch. Because there will always be another time you need them to go above and beyond the call of duty for you.
Doing these things will never make working late, early, through lunch, or on weekends 100% better. But it will be better than it could be, and they'll know. Pretty soon, they might not want to work extra time or go above and beyond for just anyone, but they will want to do it for you.