How does Paul make it clear that he is talking about the Church, the Body of Christ?

Paul makes it clear by almost always qualifying the present-day Church as the Body of Christ, adding phrases such as 'the Church, which is His body.' This distinguishes the Church, His body, from other called-out assemblies (ecclesias) also called churches, making clear he means the Body of Christ.

Les explains that the word 'Ecclesia,' from which 'Church' is translated, is used in different manners and ways than just the Church, the Body of Christ. Stephen called Israel in the wilderness around Sinai the 'Church in the Wilderness,' and a riotous mob in Ephesus was also called an Ecclesia, though translators rendered it 'assembly.' So the word church does not automatically mean the Body of Christ. Paul, however, almost always qualifies our present-day Church as the Body of Christ, or says 'the Church, which is His body.' That qualification makes a big difference. Jesus also left the church out of Matthew 25 because it was still a secret, but Revelation 19 shows the bride, the church, will be with Him.

How can you tell when the word "church" means the Body of Christ?

The word 'church' translates Ecclesia, which can mean any called-out assembly, not necessarily the Body of Christ. Paul almost always qualifies the present-day Church as the Body of Christ, saying 'the Church, which is his body.' Without that qualification, it may refer to Israel in the wilderness or an assembly.