If your Tumblr blog is to be the start of a conversation rather than the virtual equivalent of talking just to hear yourself, you have to give your readers a way to get in touch with you beyond simply reblogging your posts and hoping you'll notice. Adding a link to your email address on your blog's front page is one way to do this, though it has both upsides and downsides.
Adding the Link
Log into your Tumblr dashboard. Click the "Settings" button and select the blog to which you want to add the link, and then click "Customize." In the Description field, type the standard email link code, as in the following example, replacing "email@example.com" with your email address:
Click "Save" and then click "Close" to return to the dashboard. Your blog now has a link in its sidebar area which, when clicked, launches the default mail program and opens a blank message addressed to you.
Clicking on the link to send you an email won't work for people who only ever access their email account through a Web interface. To make it easier for webmail users to get in touch with you, consider changing the link text from simply "Email me" to "Email me at firstname.lastname@example.org." Stating your address outright means people won't have to look at the link's destination to figure it out.
Adding the link to your Tumblr gives your readers a way to get in touch with you through a method that's familiar and convenient instead of having to use the site as an in-between. Tumblr's messaging system is also somewhat prone to losing messages and doesn't keep track of what you've sent, increasing the chances that part of a conversation will go astray.
Sharing your email address with the entire Internet may not necessarily be a good idea. Spammers regularly harvest email addresses from websites, so publishing yours may result in a sharp increase in the amount of spam you get. This may not be enough of a disadvantage for you, especially if you have a good spam filter. If nothing else, though, consider creating a throwaway email account, configuring it to forward to your main account and posting it on your blog instead, since you would be able to simply abandon it if necessary.