You could learn to service a watch from YouTube. But you will to buy equipment, and you are likely going to cost yourself a penny during the learning process.
For more common movements there is no reason your local shouldn't be able to help you. However, even my local guy sends his Rolex away to get serviced. That said, some people don't like sending there watch to Rolex. Rolex likes to put things back to original in a way that some people feel is over the top or take away from the character or charm of the watch. I know that where I live there are some service centres that have been in business working with luxury vintage watches for decades, with more or less perfect reviews. You might want to find one of these if you choose to pass on sending your watch back to Rolex.