How do you say "put"?
It looks like there are several different words for the verb "to put" in Polish:
I just want one or two nice generic words that I can use to say things like "put that on the table" or "put this in your pocket.
Generally the verb is "położyć" or "postawić" Put that on the table - Połóż to na stole/Postaw to na stole. The difference between these two verbs is that "położyć" means to put in laying position and "postawić" means to put in standing position. But in many situation you can use these two verbs alternatively.
But in this second sentence you will use the verb "włożyć", because it means "put in" Put this in your pocket - Włoż to do (swojej) kieszeni.
Yes, it sounds weird.
I think that everyone would know what you mean but it sounds very weird. I'm not sure (because I'm not a linguist only a native speaker) but I think that it's not correct to say "połóż to do kieszeni".
You may use also a verb "umieścić". Than you can use it in both situations: Umieść to na stole Umieść to w kieszeni But.... A verb "umieścić" is like English "place" or "collocate". So it's used less frequently. But still "umieść to w kieszeni" sounds less weird than "połóż to do kieszeni".
Yes, just like sylwuskak said, that just sounds wrong. The thing is Polish has a lot of different verbs based on a common stem and therefore closely related. In most cases you can't use them interchangeably as they carry various meanings even if centred around a similar concept or general idea. In case of "putting" they would be:
włożyć położyć nałożyć założyć przełożyć przyłożyć wyłożyć obłożyć dołożyć odłożyć ułożyć rozłożyć złożyć
To confuse you even more, there's also the verb "cudzołożyć" but this stem is only visually the same, its genesis being rather related to "łoże" (a bed) than the action of putting, even though imagination could also go as far as connecting the two. ;)