What type of application a foreign potential spouse needs to prepare in order to be legally in the US and marry a person with dual-citizenship?
Most countries recognize marriages performed in other countries, and the US is no exception. The couple can marry in any jurisdiction that will marry them.
The advantage of marrying in the US is that they will not need to get the marriage license legitimized before presenting it with the application to the US federal government. This may be a relatively small benefit.
The Italian nationality of one party may affect their ability to marry in Italy under Italian law (I do not know the requirements to get married in Italy), but it will not have any impact on recognition of the marriage in the US.
The specific steps to legal residency depend on whether the foreign fiancee is already in the US (and, if so, in what status), and on whether the couple decide to marry in the US or elsewhere.