Baikonurin avaruustukikohdasta Kazakstanista laukaistu Sojuz-kantoraketin kuljettama lasti saapuu maata kiertävälle kansainväliselle avaruusasemalle keskiviikkona.
The subject is lasti..."cargo"...[Aside: I notice in the lead-in to this story the word, rahti, was used...so a little "vocabulary bonus"...

The verb is, saapuu...saapua..."to arrive".....everything else is explanatory.
So here it is in English as literally as I can make it:
"From space centre of Baikonur from Kazakhstan launched, carried by Soyuz booster rocket, cargo will arrive to Earth circling international space station during Wednesday."
The essential sentence is: "The cargo will arrive Wednesday." There is a string of adjectival elements...a past participle clause with an elative object and an agent participle clause with genitive elements....modifying the subject noun, lasti. The indirect objects after the verb pretty much follow the same pattern as in an English sentence.
Standard English would be:
"The cargo, carried by a Soyuz booster rocket launched from Kazakhstan's Baikonur Space Centre, will arrive at the Earth orbiting international space station on Wednesday."
I think I've parsed this correctly?? Any improvements??...
