After Effects - Making a compilation
If you are trying to do editing, you are using the wrong program.  Adobe After Effects is an effects and compositing program.  It is designed to make alterations to clips of video that can then be used together.  It is not designed for editing clips together.

If you wish to do video editing, you want a piece of software known as a Non Linear Editor (or NLE).  Adobe Premiere is the NLE in Adobe's software line.  Adobe Bridge allows for you to move back and forth between them, so you can include an After Effects composition as a clip in Premiere or open a clip from Premiere in After Effects to do effects or composition work on the clip.

As a bonus, note that this same kind of interaction can be used with Adobe Encore to add a Premiere Sequence directly to an Encore project if you wish to make a DVD or Bluray disk from your videos.

Update: Since you asked about it, here is a list of the major Adobe CC applications and their purpose.


Photoshop: In depth Image Manipulation
Lightroom: Photo cataloging, Non-destructive RAW processing and basic touch up, workflow management, printing, publishing.
Premiere: Non-linear Video Editing
After Effects: Video effects and compositing
Encore: DVD/Bluray disk production
Prelude: Video/Asset intake
SpeedGrade: Color grading
Illustrator: Vector graphic creation and editing
Flash: Vector and sprite based animation, script-able and interactive capable as well as supporting video playback 
Audition: Audio Editing DAW
InDesign: Print layout
Acrobat: Public document finishing, creates PDFs
DreamWeaver: Web design
Muse: simpler web design
Fireworks: Alternate image manipulation application, primarily targeting the web.
Bridge: Minor Adobe product that interconnects the applications to allow them to exchange nested data
Media Encoder: Minor Adobe product that allows for a shared render queue and encoding of final assets