With Twitter they offer 4 different types of social media buttons for your website. There is the ability to share a link, a follow button, a Hashtag button, and finally a mention button.
Twitter share a link button
Visit the Twitter share a link button page, then type in all the details for the page you'd like to share.
Then you need to copy and paste the code into your page where you'd like the button.

Now we can see our Twitter share a link button, and if you click it shows the details we typed in.

Twitter follow button
Visit the Twitter follow button page, and select the Twitter handle you'd like the button to follow.
Then copy the resulting HTML code and paste it into your webpage where you'd like the follow button.

Now we can see our Twitter share a link button, and the new follow button we just created. If you click on our new follow button, you can see that it will bring up the Twitter handle that we entered into the form.

Twitter hashtag button
Visit the Twitter hashtag button page, and fill out the details you'd like to use with your hashtag button.
Next copy the HTML code then paste it where you want the button on your site.

We've now got our Twitter share a link button, the follow button and the new hashtag button we created. When you click on it, you'll see the hashtag and details we typed in, in the pop-up window.

Twitter mention button
Visit the Twitter mention button page, then fill out details you'd like to use.
Then copy the resulting HTML code and paste it where you'd like the button to display on your site.

Now we have the Twitter share a link button, the follow button, the hashtag button, and the new mention button we created. When you click on it, the message you typed in will be presented for you to submit.