About a month ago, users started seeing a toggle in the Skype which was supposed to make it possible to send and receive SMS on Windows and Mac computers. While the option was visible, it wasn't functional at the time, but the Skype team has now announced that it's gradually rolling out the experience to Skype Insiders.
SMS Connect will only be available to those using Android phones for now, and being a slow rollout means that even then it may take some time for you to see the feature - our test devices don't seem to have it, for instance. If you're among the chosen ones, you'll need to navigate to the app's settings, and then choose 'Messaging' and then 'SMS'. From there, follow the steps to pair your phone and desktop device, and you'll be ready to go.
Once your devices have been linked, SMS Connect will let you respond to both one-on-one and group conversations as well as start new ones. You'll also be able to view MMS messages, but based on the choice of words, it doesn't look like you'll be able to send them, which isn't a surprising limitation.
Microsoft also warns that SMS Connect doesn't replace the SMS experience on your phone, and you can continue using your preferred app for it. Skype will simply enable the link to your computer so you can easily respond from there as well. As mentioned above, the feature is available for Skype Insiders running version 8.30 of the Android app, and it should work with desktop devices running Windows and Mac. It's currently unknown when iOS users will be able to make use of it as well.