"I am waiting for my wife."
Translation:Čekám na ženu.
"Čekám na mojí manželku" is definitely wrong, even if some half-literate Czechs might write it this way.
The correct form of this sentence would be: "Čekám na svoji/svou manželku." Note that you must use "svůj" if the possessive pronoun matches the subject. Also note that it's "moji/tvoji/svoji/naši/vaši" with a short "i" in the accusative.
Also note that Czech uses possessive pronouns less than English, that's why the "my" is redundant here in Czech.
So, just to clarify for me (a bit thick-headed this morning), specific prepositions go with specific verbs. They don't "stand alone" as they do in English. "Cekat na" vs. "Starat se o" (although both na and o mean "for" in these cases). So you really have to learn the preposition as a part of the verb it agrees with. Correct? Sorry if this is too basic a question but I'm just launching into this lesson.
How exactly do prepositions stand alone in English? Anyone who learns English must remember to say "care for" but "look after". There's no inherent logic or a strictly defined meaning in prepositions in any language.
For example, to "wait for" in German is "warten auf" and the preposition auf is equivalent to on in spatial expressions, just like Czech na. In Spanish or Finnish, the verb "to wait" (esperar or odottaa, respectively) takes a direct object, without any preposition.
The point is, this is not a feature of Czech. Whenever you learn a new verb in any language, you also have to learn which prepositions (if any) and also which cases (if the language uses cases) go with it. Different prepositions (or cases) can actually produce a different meaning even with the same verb: compare English "look at" (dívat se na +acc), "look for" (hledat +acc), and "look after" (starat se o +acc). Or a Czech example: "stát za +accusative" means "to be worth something", while "stát za +instrumental" means "to stand behind something", or "stát na +locative" means "to stand on (the top of) something".
The preposition "na" means "on" in its most basic "meaning", which is usually applied in spatial expressions - e.g. "na stole" = "on the table", "na zemi" = "on the ground" - but even so it can easily be mismatched: "na Moravě" = "in Moravia", "na univerzitě" = "at the university". In non-spatial expressions (such as "čekat na") it will correspond to a number of English prepositions (or prepositionless expressions).