Summarize:

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.
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.