An interesting question was raised by a colleague recently:
Craig, How do you start an IM session from a link on a web page?
We all know that you can create a mailto: link that users can click to open their Outlook (or other mail) client and automagically pre-populate the to: field with your email address, but did you know you can do the same thing with Skype for Business?
Skype for Business
To create a clickable link that automatically opens a Skype for Business chat window to you, or anyone else for that matter, use the following format:
<a href=”sip:craig.chiffers@contoso.com“>Click here to IM me via Skype for Business</a>
Here’s how it looks: Click here to IM me via Skype for Business
The text in purple is the SIP address where you want to send the IM. The orange text is what will appear on the web page or within your email signature as the clickable link. You can even get fancy and use a picture or Skype logo if you wish! To do that, simply use the following:
<a href=”sip:craig.chiffers@contoso.com“><img src=”skype-logo.png“> Click here to IM me via Skype for Business</a>
This time, the green text points to the location of your Skype logo, or any other icon that you wish to use.
Here’s how that looks: 
Microsoft Teams
Right now, Microsoft Teams doesn’t support the ability to directly start a chat session with a user from a link. I imagine that if/when this is introduced, it will look something like the following:
<a href=”msteams:craig.chiffers@contoso.com”>Click here to IM me via Microsoft Teams</a>
If you’d like to see this feature within Teams, vote for it over on UserVoice!
A Few Things To Note
For the above to work, the user will need to ensure they have Skype for Business installed. If they don’t the links won’t work. Federation will also need to be enabled if the user is outside your organisation.