It's easy to use some code.
On the Command button (that you already use to open the report)
On Click event line, enter
[Event Procedure]
Then click on the little button with the 3 dots that will appear on
that line.
When the code window opens, the cursor will be flashing between 2
already existing lines of code.
Between those 2 lines, write:

DoCmd.RunCommand acCmdSaveRecord
DoCmd.OpenReport "ReportName", acViewPreview

Change "ReportName" to whatever your actual report name is (surrounded
with the quotes as above).

Exit the code window. When you enter data and press the command button
the data is saved and the report will open in Preview. If you wish to
print the report without preview, change acViewPreview to
acViewNormal.