Translation:I do not go on walks very often.
I was just about to say essentially the same thing. I'm American, and we usually go for walks. To go "on a walk" sounds as if there's a particular plan. It's the same as going "for" a hike or going "on" a hike. One might say, "let's go for a hike!" or, "they're going on a hike to the top of the hill."
さんぽ ("a walk", "a stroll") is what's called a suru noun, because you can add the generic verb する ("to do") somewhere after it to turn it into a verb, making さんぽする ("to take a stroll"). That し is just part of the polite/formal congugation of the verb: する becomes します. So さんぽする becomes さんぽします.
Breaking the sentence above down:
さんぽ/"strolls" + は/(topic marker) = さんぽは/"as for strolls"
あまり/"[not] often" + しません/"do not do" = あまりしません/"[I] do not often do"
さんぽは + あまりしません = "As for strolls, [I] do not often do them.", or better English would be "I do not often take strolls."
In the descending order based on its frequency, is it sorted this way?
いつも - always
よく / たびたび / しょっちゅう- often
たいてい - usually
ときどき - sometimes
たまに - occasionally
あまり * - not often
めったに * - rarely
ぜんぜん - never
*coupled with negative verbs, i.e. あまり………ません
Are あまり and ぜんぜん are used similarly when it comes to say "not much" and "not at all" respectively when it is used as the adverb(s) for amount?