InfoPath creates "InfoPath Forms", not HTML forms. You will need to do the work yourself to turn your the form you designed in InfoPath into a fully functioning Web Form, as this is not currently a supported feature.

Microsoft has received a lot of complaints about this, and I suspect that it is something they are looking into correcting at some point in the future.

I created a form with a drop down menu and a message to pop up and then saved
it as HTML. Now the form opens up but the drop down menu is there but no down
arrow to select from the list of things I listed in there.

It works fine in Infopath but in HTML any one have a suggestion?

As Greg mentioned InfoPath does not create web forms. For this you need to either create a web form from scratch in (say) Visual Studio or use a 3rd party tool like Infoview (www.infoview.net) if you want to design the form in InfoPath and convert it to asp.net.