Here's a website: www.diversifiedhumansolutions.com

The menu works on browsers, but when viewed with my iphone, the menu doesn't have the correct appearance. How do I correct this?

Is your theme fully responsive? I'm not sure, but I don't think that VSD does responsive sites right off the bat since it does mostly absolute positioning. I don't know if there are any ways of doing it totally responsive, but I'm sure some others may have some ideas for you. Most likely though it's not responsive right now and that's why it doesn't work correctly in all browsers.

Just so you're aware, it doesn't work correctly on iPad either. At first it seems to, but if you open it in an iPad in horizontal placement and turn it so the iPad is vertical it no longer fits the screen. If you then turn the iPad back to horizontal it is not the same as it was before. Most likely this is because it's not truly responsive and you don't have different settings setup for the different variations of viewports which is what responsive design does for you.

Hopefully someone that uses VSD will chime in here to give you more info, but default VSD doesn't do responsive sites so you won't get the right look on all devices due to that issue.

I'm not where I can get a signal for my phone right now, but to confirm, VSD will not do responsive sites. Even if you add a responsive menu to a VSD site it will most likely not work correctly. It may even do 'odd' things!

VSD won't work with Responsive Design elements.
You might want to consider a separate phone/pad version of the site.

The other thing you could do with a VSD site is lay it out in thirds (horizontally), make each section 320px to fit on most phone screens. Keep text large enough to read on smaller devices. Something like this:
[ vertical menu & important/contact/ info] [main content] [additional content/photos]
The menu and most important items will display on all screens, the first and second section will display on pads and small screens, and the entire page will of course display on laptops, etc.
On smaller screens, one can just swipe left/right to bring each section into view rather than having to do a lot of pinching/zooming/scrolling. Consider using next/back buttons to make it easier to navigate through content-heavy sections.