First of all, there's a way of producing a teaser without altering any code. Just enter a 'more' tag into your post at the point where you want the post content to end when it's displayed as a list. You enter a 'more' tag into your post by editing the post, putting the insert cursor at the point in the post where you want it to break, and clicking on the 'more' tag button (just to the right of the 'unlink' button) in the visual post editor.
If you really want to use
the_excerpt instead of
the_content, you need to find the template or other PHP file that is outputting the list of posts and change
the_excerpt(). Which file this is will depend on the theme you are using. It may also be more than one file, depending on how your theme is structured and whether you just want this to happen on your front page or not. You may even have to create a suitable file - again depending on what your them provides.
You should also be aware that
the_excerpt() strips all html out of the content before displaying it. This may not be what you want.
By default, only the first 50ish words of a post are shown on a list anyway IIRC.
If you want a summary that is something other than the first few words or sentences of a post, you'll need more help than I can give you here.