Algorithm of IBAN

Maybe this helps: http://en.wikipedia.org/wiki/International_Bank_Account_Number 

What is the answer?

In the wikipedia-article there is a part "Generating IBAN check digits" which explains how to work out IBAN by yourself.
Regarding  the "mod"-part the part "Calculating the modulus of a large number" may help. If you have additional questions it might be helpful to have more details on what you don't understand.

Based on my information could you please show how to generate IBAN?

You can use http://www.iban-rechner.eu/ibancalculator/iban.html to create an IBAN for your account. The result in your case should be: IBAN CH23 8072 8000 0071 8217 5
Manually calculating the checksum is no fun, but there are plenty of implementations on the web which detail the steps, such as http://www.tbg5-finance.org/?ibandocs.shtml
Be aware of the following that only banks and other such institutes may issue valid IBANs. So you should not rely on the results of own calculations but rather ask the bank for the correct IBAN for your account.

Could you please show how to generate IBAN by myself? (Manually, by hand)

Well done. Thank you.