Landgrabbing is the form of getting land. It is referred to as a "hit", "attack", "tap" and lots of other fancy names. Also the abbreviation "LG" is used to symbolize a landgrab (L being land, and G being grab). According to general Earth rules a country should only be grabbed ONCE unless under war or retaliation circumstances. When you attack whether it be a standard or planned strike you get food, money, technology points, land and buildings. But of course as with any attack you will lose military depending on who you are attacking and the defense of the other side.
There are three types of landgrabbing: (by Kaz)

The difference between Top Feeding and PSing is you do lots of SS's, they're just on big targets. PSing you do maybe one SS, and then around 2 PS's.

Bottom Feeding is based on a few key principles.

#1 - When you have a lot of troops or tanks, you lose less readiness per jets sent. So if you had 500k jets, and 500k tanks, you would lose more readiness sending 500k jets, then if you had 500k jets and 1M tanks.

#2 - You use your allies jets up more. Say you have 1M jets, and your 3 allies have 500k jets each, for a total of 1.5M jets. Only 1/4 of the 1.5M jets are available to you. Or 375k jets. So if you sent 375k out of your 1M jets, you would double your offence. If you sent all 1M, you'd only * by 1.375.

#3 - Targets are smaller, and therefore less retaliation.

The closer to the top your are, the less effective bottom feeding is.

Any strat besides techer can bottom feed, but it is normally cashers who should do it. This is because they climb up from the bottom, and need lots of defense from the indy's on the top.  So they go turret heavy. A lot of indys bottom feed. They're dumb.

To find targets :
Do a search with a two digit integer. As the game progresses you'll want smaller and smaller and smaller targets. It'll start out with you hitting people like 1/2 your NW, and drop down to 1/4 as the game goes on. Estimate how much military you'll need to send. Usually about 1/2 -2/3 of your jets, assuming you are 1/4 offence, 3/4 defense.

Top Feeding :
The principles of top feeding are.
#1 - It is the best way to gain land, because the larger a target you're hitting the more % of his land you get.

#2 - Being a huge indy on top you can afford to get jet heavy, and still have enough turrets to stop almost anyone. Especially good if you have great def allies.

#3 - You'll get into war more often. War CAN be avoided if you send a nice retaliation msg though. Not a stupid one like, "just a lg".

Basically, you'll be doing this when you're #1, and it's about 1/2 way through the game. At that stage yours scores list difference is large enough that you can see targets half your size (you being #1 and all). So you look at the bottom of your scoreslist, find a fat target, spy on him, and attack. Make sure you have good offensive allies, and really good def allies. Hell, that goes for any time :)
Standard Strike The standard strike is the normal attack used when you want to attack an opponent and capture their holdings. Standard strikes cause the readiness of those forces to fall about 18-20%, so it is best not to send too many forces for no reason. These attacks take no time beyond the two turns. Standard strikes capture between 3% and 8% of your opponent's land, along with money, food, buildings, and technology. The percentage of land you receive depends on the size of your opponent (bigger opponents yield a higher pecentage of land), but successive attacks bring lower returns. 

Planned Assault Similar to the standard strike, this attack takes place immediately but your forces will be placed in rehabiliation for about 22 hours. During this time, your forces will not be available for attacks or defense. Like a standard strike, this attack captures a variety of your opponents' holdings, at slightly higher rates. However, because of the planning, your offensive forces get a 50% bonus in attack strength. This attack is best used for challenging larger opponents.
General Landgrabbing or Retaliation
Landgrabbing Techniques