By simulation.

Get the etsimated and the variance/covariance matrix to produce many samples of the coefficients (usually from a multivariate normal, depending on the error structure you used). For each sample, collect the predicted curve ("Y") at many values of the predictor(s) ("X"). The 95% confidence band will be all the points inside the 95% precentile range of Y at each X.

First find the nonlinear least square estimates of the model parameters and then find the covariance matrix of estimates and subsequently standard errors of estimates and we can use the formula for finding the 95% confidence for estimates as in linear regression under the constraint this is only valid asymptotically i.e. for a large sample size since inference in non-linear regression is valid only for large sample size. Estimates can be obtained manually using EXCEL spreadsheet or by using statistical software like SPSS.

Sorry but no such thing as a nonlinear line. Best, D. Booth

David Eugene Booth, for a non-English speaker, a line can be something than can be drawn with a pencil, including curves. That's why I sometimes use the expression "straight line" to indicate that I don't talk about something that might be curved...

Being a bit nitpicking, I'd say that there is also no linear line. A model may be linear or nonlinear in its parameters, and the graph of the model may be curved (that is, have some non-zero second (partial-)derivative).

@Prof. Wilhelm, I taught native English speakers statistics for over 30 years. You would not believe how many times I heard from students and colleagues about nonlinear trend lines, etc. I don't believe that this is a language problem but rather a thinking problem I had the pleasure of meeting Eugene Wigner in the latter years of his life. I also had the pleasure of meeting Max Delbruck. Neither one of them ever made a slip like that. Is it any wonder that many statistics authors confuse linear statistical models with straight line regression or the words multivariate and multivariable. In my view these things have little to do with language skills and everything to do with understanding concepts along with poor teaching and understanding within the profession. This is one of my major concerns. As always, best wishes to you, David Booth