You'll be presented with a list of results. Wait for the page to open and the video to begin to buffer/load. Look directly to the right of the user's username area.  You'll see the Subscribe button there.

Summary:
Open your web browser. Go to the YouTube homepage. Log in to your account, if you haven't already done so. Click the search term area of the page. Type a search term for either a video or a username. Click the video name of the applicable video you'd like to view. Locate the user's name slightly above the video. Click the “Subscribe” button.