The Import/Export Wizard creates a file called .DTSX. This is your SSIS package. An SSIS package is a text file filled with a bunch of XML. Contrast this with something that ends in .EXE/.COM which is an executable that any windows machine will be able to run.
We need something to consume that .dtsx file and perform the ETL operations described therein. There are three options open to you: dtexec.exe, dtexecui.exe, and custom .NET code. dtexecui is just a graphical wrapper to the command line so really, your choices for running packages are the prebuilt command line utility or custom code. Running a package via dtexec can be as simple as dtexec.exe /file C:\MyPackage.dtsx
Since you want to run this from the context of SSMS, then you'll need to either Create a SQL Agent Job or create a stored procedure that calls dtexec. Since you're new to the whole business, the Job will provide the lowest barrier of entry.
In your SSMS, connect to an instance and navigate to the bottom. You should see "SQL Server Agent" Expand that node and Right-Click on "Jobs" and choose New Job. In the Steps tab, click New.... Change the Type to "SQL Server Integration Services Package"
Pick your source (file system or SQL Server) Fill out the server name or where the package lives and you should be good to go.
One very important thing you will need to know is that Excel drivers are only going to work in 32 bit mode. This means you will need to use the dtexec.exe that exists at C:\Program Files (x86)\Microsoft SQL Server\XXX\DTS\Binn\dtexec.exe
To get that behaviour from the SQL Agent job, then you will need to add the /X86 option to the command line like

The x86 flag only works for SQL Agent job calls. From the command line, you must use the correct version of dtexec.exe