Lengths and linewidths both set the frequency of the antenna, so choosing the lengths without the line widths would get you "sort of close" to the right frequency.

Only very expensive computer programs can get you all the details you need.

Get a VSWR test setup going.
Pick a dimension line width that's easy to build and start changing the PIFA dimensions while looking at VSWR.

Those antennas can be a bit sensitive. Your results change with the size of your groundplane since the PIFA structure actually isn't an antenna, it's a tuning mechanism to get your ground plane to radiate efficiently. If you're doing some empirical VSWR tuning, in addition to the PIFA dimensions, have some metal tape to change your ground plane length to see the effects.

kch

If you do a search an look at the various PCB IFA antennas (mostly at 2.4 GHz), you will see that the width varies quite a bit, but the general dimensions. The IFA antenna that appears in a Freescale app note for 2.4 GHz has a wide trace width, and from actual real-world range testing, it seems to work better than most of the other ones.

I've assumed that when you look at the antenna as a resonant circuit, the path from the feed-point back to ground is an inductive loop, and the stem is a capacitor. If you want the Q high on a resonant circuit, get rid of resistance. For the F antenna, make the inductive trace wide.

Higgler is right, without simulation software, you can only guess, or cut-and-try (if you've got a network analyzer). But, Ansoft Designer SV (Student Version) is too limited to do a IFA antenna - I've tried. The real version would keep some manager from having a company car, so most engineers have to do without.