Old Faithful - the #1 attraction in Yellowstone - and the #1 thing you should NOT miss. Not just because it's Old Faithful, but because the whole area is literally filled with geysers, fumeroles (holes venting steam), and hot springs/thermal pools. It's gorgeous, it's amazing, and not a thing of it is man-made (except the boardwalk for safe access).
Old Faithful is located in the Upper Geyser Basin in the south-western section of the park. The first thing you should know is you aren't the only one trying to see this area... so is half the world, so be prepared for crowds... There's a huge parking lot - often mostly filled - a huge gift shop (make that two gift shops) - that are filled when Old Faithful's not going off - and two lodges, various restaurants, etc. There's also a Visitor Center. Start there as they will tell you when 5 different geysers (the predicted ones) are expected to go off (give or take a few hours) - and can answer questions, etc. There's also a couple of free movies to watch about the park.
Old Faithful - the most predictable large geyser, but not tallest or most active of all geysers, goes off every 90 minutes or so for a duration of 2-5 minutes. It's tallest shortly after the start - tending to reach heights of 100 - 180 feet - pending the individual eruption and wind, etc. They have wooden benches to sit on while awaiting an eruption. See it, then, have water, comfortable shoes (of any sort - it's all boardwalked or paved) and set out to see nature at some of her finest.
The common misconception is that Old Faithful is by itself - it's not - there are several geysers that you might chance to see going off. You can hike a good 2+ miles (one way) seeing various thermal features if you so choose. We did... and were fortunate enough to see Old Faithful, Grand, and Lion all going off at roughly the same time - as well as many others along the way, some going off, some bubbling and gurgling. The farther out you go, the less people you tend to come across.
Many people think they'll spend an hour or two here - and end up spending the day - or wishing they had more time. Plan accordingly! If you plan to spend money on a lodge, these are a couple I'd consider for the prime access to these thermal features!