If you are speaking English as a second language, I highly recommend leaving the 't' silent. I tested this on some friends. If I say 'acts' slowly and distinctly, they could hear the 't', but just barely. It is a hard combination to make, even for a native speaker. If I was speaking at normal speed, informally, I would tend to leave out the t. People who are learning English and try to pronounce the 't' end up pronouncing a second syllable: ack-uts. It sounds much more natural simply to leave out the t and pronounce it like 'acks'. People will understand you and it will actually sound better.

Sasha, The T is not fully pronounced. It is combined with the S to form the TS sound. The "ts" is a combination sound similar to the Russian ц. Akt...singular Ak(ts) The TS sound: Let's that's effekts objekts two different sounds -the Acts of the Apostles....akts -the Ax of the Apostles .....aks

After experimenting just now I discovered I pronounce those words the same as if they were spelled with an x instead of ct. Don't know if that helps.

The "t" is certainly pronounced. Take a look at this online dictionary: thefreedictionary.com There, you can listen to sound files which show you how to pronounce many of the words, both in American and British English.