Once you finish editing your images you can export your as a full quality and save it to Drop Box Or Google Drive.
Emailing the Images direct from the Lightroom is another option. Refer: Email photos
You can also publish your images on the social media channels as well. Refer: Adobe Photoshop Lightroom Help | Post photos online using publish services
Saving the Image to the Drop Box or Google Drive is the easiest way to share high quality images with your friends & family.
Hope it helps.
So does this mean that Adobe does not offer a similar in app service to that of google drive or drop box. Do I have to export to a 3rd party app if I want to upload full quality images to the web to share with others? Like I say, I want to be able to to do this from inside light room.
Adobe does offer Cloud service with the app, You can use the Lightroom Mobile app, where you can sync your images from your Lightroom Desktop to Lightroom mobile but it only sync the previews for the images which is only good for editing using the mobile app.
You can buy the subscription for the creative cloud which offer's you 20 GB Storage (Single App Membership Or Complete membership) but again you need to export your images out from the Lightroom and save it to Creative Cloud folder just like Drop Box Or Google Drive.