Roland is right, tutorials are the way to go to get a solid foundation. Still, I understand the frustration of wanting to do just that one thing and having to wade through pages and pages, so I'll give you step by step for just that one thing. (If you're on a Mac, substitute Cmd where I have Ctrl.)
- Open AE and press Ctrl-I, and select your PNG for import.
- Create a new Comp, and set it to the dimensions and duration that you want for your animation. Then drag your PNG into the left column of your timeline, which will center your PNG in the frame.
- Press Ctrl-Y to make a white Solid for behind your logo (Click the option to make it Comp size). Drag the Solid to the bottom of the stack in the timeline to put it behind your logo.
- Select your logo layer in the timeline, and press T on the keyboard to show the Opacity property. Move the playback head to the frame where you want the logo to be finished fading in, and click the little stopwatch (left of the word "Opacity").
- Drag the playback head back to the frame where you want the logo to start fading in, then click the parameter for Opacity (right of the work "Opacity", currently be set to 100%. It's blue.) and enter 0, hit Return, and a keyframe will be created. Now your logo will fade in.
- To render your animation, press Ctrl-M (or Cmd-Ctrl-M on a Mac), to add it to the render queue. There you can set your parameters for rendering.
Hope that helps get you started for now! 