Most Android devices for some time now support the creation of screenshots. On New Galaxy Note 2 you just have to press the Lock and Home button at the same time to create a new screenshot of what is being displayed on the screen at that point in time. It takes between 1-2 seconds of pressing the buttons before the screenshot is being taken, likely to avoid accidental screenshots being taken.
Taking the screenshot is however only part of the process, as the image needs to be transferred from the phone to the Internet or web server. Here is one option on how to upload screenshots that you take with your Android phone to the Internet.
Android to Dropbox
If you are a Dropbox user you can download Dropbox for Android to link your smartphone with a Dropbox account. You need to sign in to Dropbox once to establish the connection. A wizard is displayed afterwards that walks you through the initial configuration. If you have a limited bandwidth available or pay for your bandwidth, you may want to enable Wi-Fi only uploads to avoid additional costs. You can furthermore select to upload existing photos or videos.
Once setup, all screenshots that you take using the phone are automatically uploaded to the Camera Uploads folder of your Dropbox account. It is alternatively possible to disable automatic uploads and upload photos manually instead only. To do that open the settings of the app and tap on turn off camera upload.
You can then access the screenshots either on a computer if the Dropbox client is running on it that synchronizes the files with the computer, or by opening the Dropbox site on the Internet where the screenshots are also available.