dům = house domov = home stýská se mi po něčem = to miss something (to be sick of missing something) = tęsknię za czymś Notice that the Czech reflexive phrase uses a general subject and the person is expressed with object: stýská se mi = I miss… stýská se ti = you miss… stýská se mu = he misses… … The Czech phrase works even without specification of the missing object: Stýská se mi. You can also use the non-reflexive variant with the verb “tesknit (po něčem)”, but that’s rather bookish.
It's also possible to say "chybí mi..." or "schází mi" (these two are synonyms). For example: Chybí mi tvůj smích. = I miss your smile. While "stýskat" has only one meaning, "chybět" and "scházet" have more. In the case of homesick, it is possible to use them, too: Chybí mi domov. Schází mi domov. In my opinion "Stýská se mi po domově" sounds better It sounds like the author really is homesick.
On the subject of missing something or someone: My brother-in-law that died in a fire about 7 months ago had a broken necklace of stones. I'm using those stones to have a ring made. I wanted to engrave "I miss you Adam" I planned on using Chybíš mi Adame but is another way more poetic or sound stronger, like to long for him or really hurt from his absence?
Sorry to hear that, Dzurisova :? I think Chybíš mi, Adame is great for this situation, but let's hear another opinions from the other Czech people here.