Sujud as-Sahw in prayer is prescribed for three reasons: 1- Doing something extra, 2- Omitting something, 3- Being uncertain. Sujud as-sawh should be done before the salam if you have omitted one of the obligatory parts or you are not sure how many rak`ahs you have done. Sujud as-sahw should be done after the salam if you have added something extra or you are not certain but one of the two choices seems more likely to be the case.

There is no tashahhud after Sujud as-Sahw because the Messenger of Allah (peace and blessings of Allah be upon him) did not do that, as is indicated by the sahih hadiths.

If you forgot to do sujud as-sahw, you can make it up if you are still in the mosque and a long time has not passed. If a long time has passed or you broke your wudu or you left the mosque, you do not need to do the sujud and your prayer is still valid.