If you wish to use the ZlibStream to compress data while reading, you can create a ZlibStream with CompressionMode.Compress, providing an uncompressed data stream. Then call Read() on that ZlibStream, and the data read will be compressed. If you wish to use the ZlibStream to decompress data while reading, you can create a ZlibStream with CompressionMode.Decompress, providing a readable compressed data stream. Then call Read() on that ZlibStream, and the data will be decompressed as it is read.
A ZlibStream can be used for Read() or Write(), but not both.