Totems - The purpose of a totem is to give you a way to make sure you're not being conned by someone else. In any dreamworld, one person is the host, and everyone else is a subject. The host's mind is responsible for creating the setting and objects in the dream world. The subjects then populate the world with their subconscious. As long as you keep something specific about your totem secret, such as its weight or feel, a host will never be able to recreate it right, and this you can always use your totem as a test to make sure you're not in a deeper level of reality than you think you are.
Kicks - A kick only brings you back to the reality in which it happened, it only reaches one reality deep, and it only affects you if you're conscious in the reality the kick is trying to pull you from. On top of that, it appears that a trained dreamer can resist the effect of a kick to a certain degree based on the severity of the kick and the strength of the sedative used. When layering multiple dreams, multiple kicks are needed to work backwards through the layers. For example, the crashing elevator in the hotel level would pull those in the ice fortress level back to the hotel. Once they were conscious in the hotel level, they would be susceptible to the kick of the van crashing into the water. There was no kick planned in the airplane, though, meaning that they would have to wait in the van level for the sedative in the airplane to wear off.
Hosts vs. Architects - The architect merely designs the level needed for a mission, but the architect is not necessarily the host. It is implied that the architect, likely through other shared dreams, is able to help the actual host prepare the level he will be hosting. In the mission shown in the movie, Ariadne is not the host to any of the levels. In fact, she wasn't even supposed to go along on the mission, and only insisted on going after seeing just how unstable Cobb was. Yusuf, the chemist, is the host to the van level. (His failure to go the bathroom before getting sedated on the plane is the reason why it is raining in his level.) Arthur, the point man, is the host of the hotel level. Eames, the forger, is the host of the ice fortress level. It is implied that in a layered dreamworld, the host can't go deeper than the world he is hosting. This is why Yusuf goes no deeper than van level, Arthur goes no deeper than the hotel level, and Eames goes no deeper than the ice fortress level. (Note: Arthur is able to use the stair paradox trick in the hotel level because he is that level's host.)
Guests vs. Marks - A guest's subconscious populates a host's dreamworld. Apparently a guest who knows what he or she is doing can control this to an extent, and thus only the mark's subconscious ends up making up the majority of the world's populous. However, if another guest, such as Cobb, has difficulty controlling his subconscious, parts of it, such as Mal, can start to enter the hosted world.
Forgers - A Forger has the ability to alter his or her projection within a level. Weather or not he can do this in a level he is hosting is unknown. What special skills allows a forger to do this is also unknown, but its possible that a forger has developed a very strong control over his subconscious's sense of self. (In the van level, Eames interrupts Arthur's firing of a sub machine gun by telling Arthur that he shouldn't be afraid to dream bigger. Eames then attacks the enemies with a grenade launcher. There are two possible explanations for this... 1. Eames' forger ability allow him to create not just new personae for himself, but also new tools. 2. The teamed worked with the architect to design the van level prior to the mission itself, and it was during this shared dream planning that the various members let the architect know which tools they wanted available in the level. Eame's remark to Arthur was then simply Eame's way of saying to Arthur that next to he plans for a mission, he shouldn't be afraid to tell the architect to give him some truly impressive tools.
Time - Time in a dreamworld moves faster than time in a level above it. In a multi layered dream, this effect compounds. It is stated that under normal circumstances, five minutes in the real world allows for 1 hour in the dream world below. This is a ratio of 1:12. It is also stated that a strong enough sedative can increase this ratio. For the mission, the ratio is said to be 1:20. Thus, one hour on the airplane would be 20 hours in the van level, which in turn would be almost 17 days in the hotel level, and close to one year in the ice fortress level.
Death - Getting killed in a dreamworld typically causes one to awake in the level above where you were killed. However, a strong enough sedative can suppress this feature, and will instead send the individual who died to limbo. During the mission, Saito is shot while in the van level and slowly begins to die. When he enters a lower level, the wound is no longer on his body, however he is still slowly dieing. (He is dying at 1/20th the rate at each subsequent level, due to the time compounding effect.) When Saito finally dies in the van level, his death propagates down through all the levels and he goes to limbo. Normally he would have returned to the airplane, but the strong nature of the sedative prevented that from happening. When Fischer is killed in the ice fortress level, he does not wake up back in the hotel level, because the same strong sedative was used between the hotel level and the ice fortress level.
Limbo - Limbo is an unconstructed dream state of pure subconsciousness. It is apparently very hard for a dreamer to maintain awareness of reality and even self awareness while in limbo. The rate of time in limbo is very unpredictable, and an unprepared dreamer in limbo could find himself stuck there for a near infinite period of time. The only way it is shown to exit limbo is to commit suicide there, or possibly to live long enough in limbo for the sedative to wear off. It is also not clear if someone else can kill you in limbo to set you free, or if you have to choose to kill yourself. It is also implied that limbo is not bound by the normal host/guest rules. Multiple dreamers are apparently able to share a limbo, and with practice are able to both shape limbo to be whatever they want. The movie doesn't give much info on what a truly uncontrolled limbo is like. Its possible that the limbo during the mission would have simply been a jumbled mess of the subconscious of all the members of the shared dream. Cobb, however, has extensive experience shaping and controlling limbo, and thus is able to host limbo, (or at least part of it), as another level beneath the ice fortress level. When he creates this new level, he connects Adaidne and Fischer to himself with a dream machine in the ice fortress level, thus allowing them to be guests in his hosted limbo, and proving the pathway by which to "kick" Fischer back to the ice fortress level. The kicker that Eames uses on Fischer is to shock him with the defibrillator. This apparently provides enough of a shock to the system to trigger a kick. However, since the only way to leave limbo is to die in limbo, Fischer has to jump from the skyscraper when he detects the kick happening. Ariadne in turn has to jump from the sky scraper when she detects that Eames triggers the second kick in the ice fortress level, by imploding the fortress on itself. (When Fischer is "kicked" back to the ice fortress world, his bullet wound is apparently gone. Why this happened it unexplained, however there are several possibilities. 1. The wound was merely a flesh wound that had an unlucky side effect of stopping his heart. 2. Eames, as the host of the level, was able to alter the nature of the wound while Fischer was in limbo. 3. Once Cobb made peace with Mal, the wound she had caused Fischer was undone. 4. The act of dying in Limbo resets Fischer's subconscious self awareness of life and death, and thus when he wakes up from limbo back in the ice fortress level, his subconscious projects a new, non-dead persona of himself. (Note: Cobb, by not committing suicide in limbo, avoided the kick in the ice fortress level. He then spent an unknown amount of time hunting for Saito in limbo. It is implied that this takes many decades since Saito is now an old man, however Cobb is not old, which leads to two possibilities. 1. Limbo moves at a different pace for each person. 2. Cobb, as an experienced dreamer in limbo knew that it was all still just limbo, and this his subconscious didn't age him.) When Cobb finally finds Saito, he hands him a gun and convinces Saito to commit suicide with him, setting them both free from limbo. It is unclear weather or not their subconscious minds cause this event to happen right as the sedative on the airplane is wearing off, or if the suicide sends them to some truly unconscious state that they both wait in unaware until such time as the sedative in the airplane wears off.