You measure it by expanding the beam and seeing what you have.
In most lasers though, higher modes mean more power. DPSS lasers would be the only case where sometimes this isn't true. It really depends on the cavity design. For most handhelds, usually the TEM mode doesn't matter since all your doing is pointing them at stuff.
When lasers are used for 'real science' as I call it. Holography, particle counting, etc, is when a stable Gaussian TEM00 beam is required.
For He-Ne lasers, TEM01 is called donut-moding as the beam looks like a donut hole. it looks like a light beam with a dark spot in the middle. This is caused by destructive interference in the middle of the beam. It is especially bad when trying to make holograms.