Whilst most stores and banks will be closed on 1 August, transportation will run normally and a number of tourist attractions will be open. If you are intending something particular (a museum for example), you will probably want to check on the website. Remember it's a bank holiday and the Swiss will be making the most of having a day in the country, so roads and trains can get crowded.
The Swiss celebrate 1 August with bonfires and fireworks in the evening. If you're out in the country, just about every village will have something going on. Typically a parade with lanterns in the early evening, speeches by local dignitaries, the oath of allegiance, the national anthem, then the bonfire and fireworks. It's usually quite fun, there's plenty of fried sausages and beer. The exact offerings will vary.
In the towns the whole thing will be a bit more formal.
I would guess any hotel will be able to tell you more about what's going on locally.