I focus prior to hitting the record button. To do so, just zoom in using the magnify function. Set the focus, then hit record.
To focus during recording, things are not so easy. I use a viewfinder, which does help. The one I use is fairly inexpensive (around USD100) and is called the LCDVF. This magnifies the LCD screen and makes it visible in daylight (plus adds a bit of stability if shooting hand-held). Still, getting precise focus this way is fairly challenging. I can almost do it on my 5D3, which has a better LCD than the one on the 60D, I think.
As is pointed out many times here, DSLR's are not substitutes for traditional video cameras, especially when it comes to the need to change focus during the recording.
There are other methods that use a firmware hack, called Magic Lantern. But, that's opening up a can of worms that you might not be interested in. If you are, try searching on "Magic Lantern Focus Peaking" in Google and you'll find plenty of information. If you have questions about that, I and others here will be happy to respond.