You can set up an e-mail signature in Office365's OWA (also works with on-premise Exchange 2013 OWA) quite easily. While it's no problem to apply any kind of formatting to your signature, you'll find out that adding images is not as straight forward.

To set up an e-mail signature, follow the steps below.

For best results, use either Internet Explorer or Firefox. Google Chrome has some (minor) issues with OWA.

1. Log onto OWA. For Office365, this is https://outlook.office365.com/.
2. Click on the gear icon in the upper-right corner, and choose Options.
3. In the left tree, follow Mail > Layout > Email signature.
4. Edit your signature, or copy/paste it from another source (e.g. Word).
   If you have images in your signature, read below!
5. Click Save to save your signature. Optionally, before saving, you can check to automatically include the signature on outgoing messages.

About images in the mail signature

When attempting to copy/paste an image in the signature, at first, it will seem to work when saving the image. But when creating a new mail, you'll notice the image is gone. This is because signatures in OWA can only work with externally linked images; inline images are not supported. Copy/pasting an image directly will link that image to a temporary URL. When creating a new e-mail, that temporary location will no longer be valid, and the image will therefore appear empty.

The solution is to place the image on a webserver somewhere (one that is permanently available), then refer to that image. As long as the webserver and image are available, the image will be available in your signature as well.

If you do not have a webserver, you can use an image service like TinyPic, or the public folder of a Dropbox account.

1. Edit the image to your liking an upload it to a server so it's publicly available.
2. Now this is very important: open the image (through its URL) in your webbrowser. A quick way is to use right-click the image, then select View image (Firefox), or Open image in new Tab. The important part is that you have the direct link to the image, and not some reference to the image through a "HTTP query string":
   
3. Select the image in your browser (right-click), and choose Copy. Do not copy the URL (if you do, you'll only paste the URL as text), but really copy the image from your browser.
   On Mac, you may have to use drag and drop, instead of copy/paste.
4. Go back to the signature edit window of OWA (see above) and paste the image in the edit box, at the location when you want the image. The image will be pasted in, but the link behind it will point to the permanent location (i.e. your publicly available webserver).
5. Save the signature. Creating a new e-mail will now perfectly display your signature, in your own OWA window, but also at the recipient's end.

It's worth noting that because images through OWA are linked images and never inline, the images may be filtered out by the recipient's e-mail program - Outlook is known to do this for any sender not in your address book.