What are the various ways you capture the small and large bases in Planetside 2?
All bases are capped the same way:
To speed up capturing, have your people stand around the control point(s). Each control point has a number of people it supports to speed up capture, displayed below the control point on the left side of your screen. For a single control point, it's usually x/6, for multiple control points it's x/2.
The final speed of the capturing depends on:
How to get to the control points is a completely different matter though.
On both sides of the base are shield generators that control the main building. Destroy both shield generators to open up the way into the main building where the control point is located. Enemies usually park a Sunderer inside the vehicle bay, once the shields go down, it can easily be taken down from a disatance by Heavy Assaults on the wall.
Outside of the base are again two shield generators that control the shields. You need to destroy them if you want to get into the base with vehicles. Infantry can always get into the base from the direction of the enemy spawn, i.e. the side where the enemy turrets are on the top of the Tech Lab. There are two small doors on this side that provide access to the interior of the base where the control point is located. However, the doors are small and easily camped, so going for the wider entrance on the other side of the base - the side with the airpads on top - is recommended after you destroyed both shield generators required to gain access to that entrance.
Bio Domes are the hardest bases to capture and if the enemies had time to prepare, it's almost impossible to break through. There are four ways to get into a Bio Dome though not all of them are available on every biodome:
If you plan on capturing a Bio Dome, send infiltrators ahead to take out the SCU shield generator and then the SCU to prevent enemies from building up a defense.
Bio Domes usually feature 3 control points inside the dome, with the exception of Allatum in the west of Indar which has 4 control points.
Note: When attacking, never park your Sunderer below the Bio Dome, it only annoys the attackers. There is no entrance at the bottom of the Bio Dome. Park it near a jump pad, teleporter or - if available - a lift.
Walk up to the control points and sit on them until the base flips. Nothing special about those.
Just speaking mechanically it's always the same way: Capture a majority or all of the control points in the area (they're automatically shown on your HUD as well as your map display; smaller areas only have one, larger areas have up to three) and keep that majority while the bar designating the enemy's level of control over the area starts shrinking.
Once it vanishes entirely a bar with your faction's color will start growing, and once it's reached max, congratulations. Your faction now owns the place.
Tactically speaking, of course, the difficulty is in the whole "... and keep that majority" part; the enemy faction will likely be trying to hold on to the place and they have the advantage of respawn points right where they need to be. Make sure you can reinforce quickly by way of the mobile respawn points function of the Sunderer vans.
In Planetside 2 it's incredibly simple, so I won't try to complicate it.
Every base controlling a territory will have one or more Control Point labelled [A], [B], [C], etc on the map. You need to capture and hold more of these Control Points than the enemy, for a certain period of time (couple of minutes) and then the base is yours.