These are called swing-top bottles, and they're fine for re-use as long as they originally contained a carbonated drink like beer, and the glass has no chips or cracks. The usual advice regarding re-using commercial bottles applies here. First make sure they are clean, and then sanitize them before filling with delicious homebrew.
The easiest way to clean bottles is make sure they never get dirty. After drinking the beer, rinse the bottle before the dregs have dried out, and before any mould or fungus has had a chance to grow. If the bottles are grimy inside, a 24-hour soak in OxyClean followed with a thorough rinse should dislodge any gunk.
There are different ways to sanitize, but I find that dunking the bottles for a minute or two in a bucket of no-rinse sanitizer (like StarSan) and then draining, is the simplest and quickest.