As @homer150mw already mentioned, you have done the calculation correctly. In the future, you can avoid making mistakes of this kind (i.e., dividing instead of multiplying) by keeping track of "units."
Often, in some calculation, a number has some units associated with it; for example, 570 might be 570 kilograms or 570 kilometers per hour. You can keep track of these units when multiplying or dividing, by treating the expressions for units as fractions and cancelling as needed. For example, if you evaluate the expression "(5 kilometers/hour) * (3 hours)," the "hours" cancel and you get "15 kilometers." Similarly, "(6 kilometers) / (2 kilometers/hour)" yields "3 hours."
In your case, you can reason that your currency conversions come with units: 0.976 is actually "0.976 Swiss Francs per US Dollar." From there, you can see that you should multiply that number by a number of dollars to get a number of francs, so that the "US Dollars" term cancels in the denominator.
This type of reasoning is called dimensional analysis.
Note that, as some commenters pointed out, some places will unfortunately write 0.976 USD/CHF to mean "0.976 USD converts to 1 CHF," instead of "0.976 USD per CHF," defying all conventions about what "/" means. If you're given some number as a currency conversion rate, make sure you know what it represents. The above rationale interprets fractions as meaning "0.976 USD per CHF," as is standard throughout the quantitative arts and sciences.