How can I compute the 95% confidence interval of the ratio of two values (knowing their SD, and assuming they follow a Gaussian distribution)?

This page (from Intuitive Biostatistics, first edition) explains what to do (based on EC Fieller,
Suppl to J.R.Statist.Soc, 7,1-64, 1940).

GraphPad has created a free QuickCalcs web calculator that does the calculations.