When you are online in Skype, your contacts see a green icon beside your name. This lets them know that you are online and available to chat. You may find that this becomes an inconvenience sometimes. For example, if you are only on Skype to talk to a specific person, having others send you messages can be an annoying distraction. Fortunately, Skype offers a way to hide the fact that you are online. You can appear offline to your contacts while still sending and receiving messages.
Sign into Skype as usual. There is no way to sign in as invisible.
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Click the status icon beside your name in Skype's upper left corner. Unless you have already changed your status, this icon is green with a check mark inside. This brings up a list of status options.
Click "Invisible" in this list. As you can see on the list, the icons for "Invisible" and "Offline" are identical. This makes you appear as though you are offline to your contacts.
Change your status back when you are ready by clicking the status icon again then clicking "Online." Your icon now appears as green and your contacts can see that you are online.