There are a wide variety of different ways of getting tweets on a WordPress blog. The simplest way is that of using WordPress' own plugins - the Twitter widget and the sharing settings of the blog itself. When you first set up and begin your blog, you'll be asked if you want to add some of the widget selections that go within your blog's sidebar.
The sidebar can hold everything from RSS updates to stats about your blog to...Twitter updates. This widget basically adds all of the tweets that you create whenever you create them and who they are going to, more importantly it allows your readers who weren't following you on Twitter to click on your name or Twitter title in order to be brought to your Twitter profile.
How can this help your blog? Simple. It allows for people to find you on Twitter, thus allowing them to not only follow your tweets, but follow your tweets in regards to your blog.
Another aspect of WordPress that will help get the word out about your blog is that of the sharing settings. The share settings are where you can add some buttons that will help people share your particular blog posts to their favorite social media sites. WordPress currently has Facebook, Twitter, LinkedIn, Digg, Reddit, Press This, email, and printing.
While signed in to your WordPress account, head to the settings options and then choose 'sharing'. Here, you can also add your own accounts to help promote your blog by sharing your updates with friends and family on Facebook, Twitter, Yahoo, and MSN Messenger. This will automatically update your profiles on these whenever you update your blog. Under this is where you can add sharing buttons for your readers, so that they can share your blog to their friends and family.