With the latest Overwatch update, sharing your Highlights & POTGs are made much easier than before!
How to share your play
Open Overwatch and play a game.
After your game, go to the Main Menu, and you will see the 'Highlights' option. When that option is available, that indicates that you have Highlights from the matches you've played.
Click on Highlights and you will see all your highlights for the past 24 hours.
Next, you'll need to click on the 'RECORD' button to record and save your highlight.
Name your highlight, select your settings or keep the default values as they're good enough. Then click on RECORD again.
Your highlight will start rendering and saving to your Overwatch Documents folder. Usually C:\Users\USERNAME\Documents\Overwatch\videos\overwatch
Now grab the video file which is your highlight and upload it to https://gfycat.com/ or https://www.youtube.com/ or any other video sharing website. DropBox, Plays.tv, Twitch.tv also work.
Once the upload is done, you can share the link to the Overwatch Club.