Great question as usual.
One can divide a sentence depending on what is one's focus. For an example, below, I placed "/" between the each divisible segment of the sentence:
正し/い/字/を/美し/く/書/く/ため/に/は/正し/い/筆順/で/書/か/なければ/な/り/ません。
Tadashi-i ji-wo utsukushi-ku ka-ku tame-ni-wa tadashi-i hitsujun-de ka-ka nakereba na-ri masen.
In the above, I disected the sentence according to all the grammatical rules I can imagine.
For an example, "tadashi" is the root of the word meaning "correct" that can be an adjective by ending with "i", and adverb by ending with "ku".
"Ji" is a noun meaning "letter" by adding a particle that defines if it is a subject or an object such as "te, ni, wo wa". "Ka-ku" is a verb meaning "to write" and "ka" is the root that can be followed with different suffixes depending on tenses and terms.
Basically, you will start seeing separation of words clearly as you gain more vocabulary and grammatical knowledge.
Keep up your great work! 頑張ってね。