There are a number of different ways you can record the tracklog. If you are in a vehicle, plane, boat or whatever, you can put the iPhone in a dash mount and plug in a power adaptor. But for handheld use, you need to consider battery life, and the possibility of unintentional screen touches.
If you want to see the screen, but you don't want any accidental touches to interact with the application, press-and-hold the GPS Lock button on the toolbar for 4 seconds. This will lock the screen, so that the application ignores any touch events. There is a small button on unlock.
Memory-Map has the ability to use the GPS and record a tracklog while the app is in the background, or even with the screen turned off. You can enable this option in the Settings > GPS Settings dialog.