Create a theme for personal use in Tumblr

1. Go to the Customize section after you log in
2. Click on the Theme tab
3. Click Use custom HTML

This will bring up a edit box that contains the HTML and tumblr code used by the theme.

Put the code for the tags somewhere between the opening {block:Posts} and closing {/block:Posts} tags.

To start off easy, let's put the tags at the bottom of all your post types.

Where you see the following line:

{/block:Posts}

Insert the following starting chunk to look like this:

    {block:HasTags}
       {block:Tags}
          <a href="{TagURL}">{Tag}</a>
       {/block:Tags}
    {/block:HasTags}

{/block:Posts}

1. Click Update preview in the lower right corner of the edit box (or it will update itself)
2. Click Save + Close in the upper right of the dashboard.

Refresh your tumblr blog and you should now see the tags display.

You can read more of the specific tags markup needed on the Tags section of "Creating a custom HTML theme"

I've got another idea.

{block:Tags}<a class="tag" href="{TagURL}">{Tag}</a><span class="tagtail"></span>{/block:Tags}

This will add a span with the "tagtail" class after every tag.

Then, add this css:

span.tagtail + a.tag:before {
   content:", ";
}

This will select every tag anchor that comes after a tagtail span (so every one but the first). This way, we avoid the need to use the first-child or last-child selectors.

UPDATE:

If you want to ensure that the commas are styled apart from the anchor, I suppose you could also do:

{block:Tags}<span class="taghead">, </span><a class="tag" href="{TagURL}">{Tag}</a>{/block:Tags}

and then style it like:

span.taghead { display:none; }
a.tag + span.taghead { display:inline; }

However, this might need tweaking because browsers differ on overriding rules.