Team Sneak mode has one team playing with stealth camo and stun weapons, trying to grab the target and place it in the goal. The other team has live weapons and the defender's position, to guard the target until time runs out or all attackers are defeated.
Rescue mode is the same, except both teams use equal equipment. In both modes, there are no respawns by default, so you only get one chance, which calls for tactical strategy instead of just running in shooting. If you act like it's a simple Team Deathmatch, you'll lose every time.
As defenders
In Team Sneak, the attacking side gets stealth camo that renders them invisible to defenders, except for their shadows and weapons. Defenders will want to look for floating weapons and attackers will want to switch to their knives for a smaller weapon, and stay low and in the shadows as much as possible. Sloppy sneakers will just run up thinking themselves invisible, and once they're shot, all members of that team will lose their cloaking as well.
As defenders, your team will want to cover all possible access points leading to the target. Traps can be used to either catch enemies or at least to reveal themselves if they disarm the traps. Try to stay just around corners where you can't be seen and watch the approach path with the third-person camera. Have your aim ready at head height and jump out shooting when an enemy approaches (or you see a floating weapon). As a defender, you have all the time; don't get impatient, just watch your spot and wait. If you hear your teammates being taken out at other posts, then you know which way the attackers are approaching and can move to a new position.
In Rescue mode, beware of clustering together while defending; the attacking team will throw grenades into the middle of your group. Snipers make good defenders if you can find a spot with good visibility. Hiding in trash bins, cardboard boxes, and oil drums will often let you take attackers by surprise if you stay still and in an inconspicuous location. Wait for attackers to pass by before jumping out from cover.
As attackers
Don't bother with stuff like traps or snipers, since all the defenders have to do is wait you out and they win. Take the offense, but be smart about it. Make sure the SOP system is activated at the start of the round to keep tabs on what's going on in your team.
In Team Sneak, you want to use your smoke grenades to cover your approach to the target, but don't use them too early or you'll just be giving away your approach. If a teammate is spotted everyone loses their cloaking; if that happens, hide as fast as you can until the alert status is gone. Once you grab the target, run for the goal. Alternatively, if your team can take out all the enemies you win as well. It's hard to do with stun guns against the real thing, but it's an option.
In rescue mode, attackers will want to use grenades take out enemies hiding behind cover, or Electronic Locators to reveal where they're waiting. Too often, eager teammates will just rush in and get killed, forgetting that they don't respawn. Stay back and let such ones draw enemy fire so you can see where they're at, then get the drop on them while they're reloading from shooting down your eager teammate.
A final note about ghosts
To keep fallen players busy, since they can't respawn, MGO offers a "ghost prank" option that allows players to stand up as translucent ghosts after being defeated. They're codec messages turn spooky and they can see -- and bother -- players still alive. It's quirky fun, but since players can see the ghosts on both sides, fallen teammates can essentially hang around hiding opponents to reveal their position.
Of course, experienced players turn that option off, since it ruins some of the sportsmanship of the game. But if it's on, you might as well look for -- and provide -- ghostly help.