One way to say that it is half past the hour is to use the word for half which is половина. Since the hour between 12:00 and 1:00 is considered the first hour, 12:30 is половина первого. You will notice that первого is in the genitve case. That's because there is an implied часа after it. That is, you are implying that the time is “half of the first hour.” 1:30 is «половина второго» “half of the second (hour)”. Here is a complete listing of times on the half hour as expressed with половина.

There is also an abbreviated way of saying the same thing where «пол» a morpheme meaning “half,” combines with the genitive ordinal number to make a single word that indicates half past the hour. That's right: Russian has a single word that means “one thirty,” and another one that means “two thirty,” etc. Here's a complete listing.

Other entries dealing with time are soon to come. Look for them under the categories "Time phrases" and "What time is it" and "At what time."