"I go for a walk in the park often."
"masu" is added to the end of many verbs to make them into the polite or humble form. 食べる, "eat", becomes 食べます in the polite form. 飲む, "drink", becomes 飲みます in the polite form. In those cases, it is simply part of a word and not a whole word, like "s" in the word "eats" or "drinks".
sanpo s.uru belongs to a group of special words. Nouns or other word classes, most of Chinese origin -but not only- can be formed to verbs with suru. They form a kind of noun-verb-compositional word. Benkyo (study (noun))+suru = to study (verb). There are thousands of these words. Since they are related, they don't need the particle "wo". However, they can stand with it.
Thanks to English grammar, "time words" can go almost anywhere in a sentence and still make perfect sense. For instance, "often i go", "i often go", "i go often", "to the park often", and of course "for a walk often". Replace often with "rarely"; and, using commas in some cases, with "at 3 o'clock", "at sunset", etc.
This one is an important character, as other commenters have discussed; します is always either being used as a separate word with を or as the conjugation of certain loan words, and in either case simply ます is not correct. It would be kind of like saying, "i take walk at the park often". At first glance it looks okay, but then you realize you've forgotten something. (In this case you need to either pluralize walk or use the nonspecific article "a").