The About Me widget, often placed in a sidebar, can be a great little tool to welcome visitors to your site and introduce yourself. The widget area is a bit small, though, if you'd like to write a substantial amount of text. One option is to add a "Read More" link at the end of your short "About Me" widget text which will link visitors to your "About" page should they wish to continue learning about who you are in more detail.
Navigate to Appearance > Widgets > Set up your "About Me" widget as you'd like.
After the bit of text you enter into your widget, copy and paste the following bit of HTML code:
<a href="your-linking-URL-here">Read More...</a>
Please be sure to replace the dummy "your-linking-URL-here" text with the URL of your "About" page, or whatever page you'd like to link visitors to via this link. In the above code, we've set the wording to say "Read More..." though you are very welcome to change this to say whatever you'd prefer.
Be sure to save changes to your "About Me" widget when you're done.