I recently developed a web site geared toward portable devices, and after working with iOS Xojo for a couple month, I was sensitized to the particular issues portable devices create.
Rainer Morgen is already close to what you need, if you assume users will always hold their devices in Portrait mode. Hos template offers screens for most of the devices available, including desktop. By monitoring the screen size in each webpage, you can switch to the appropriate one.
You may also want to design webpages for Landscape mode, still manages in the resized event, so if the user rotates the device, you can present a better layout.
Another thing to think about is if you need data entry, make sure to place textfields and textAreas on top of the screen so when the user taps in the entry fields, the keyboard does not mask them.
Make sure to dimension the buttons and control so they are easy to use with fingers. Some controls are not terribly easy to use with touchscreens, make sure to test on a device.
When you debug, you can access your running application from the phone or tablet by typing the address of the computer on the network. For instance http://192.168.1.55:8080 (instead of http://127.0.0.1:8080). On Windows, you can find that address in the Network center, in Mac, select the Network preferences, then click Advanced, click TCP/IP. The address is the IPv4 address.
Finally, the design of your app can be more familiar to users if you try to emulate the devices interface. The iOS App anatomy page is an interesting read https://developer.apple.com/library/ios/documentation/UserExperience/Conceptual/MobileHIG/Anatomy.html#//apple_ref/doc/uid/TP40006556-CH24-SW1
Using a tab bar with the same kind of icon design as iOS8 can greatly improve the navigability, for instance. On iPad in Landscape mode, you can emulate the regular iOS iPad tab bar with a vertical rectangle alongside the left of the screen.