How can I create a zip file by using Objective C?

I definitely recommend Objective-Zip. It just recently moved to https://github.com/flyingdolphinstudio/Objective-Zip:

Some examples from their documentation:

Creating a Zip File:

ZipFile *zipFile= [[ZipFile alloc] initWithFileName:@"test.zip" mode:ZipFileModeCreate];

Adding a file to a zip file:

ZipWriteStream *stream= [zipFile writeFileInZipWithName:@"abc.txt" compressionLevel:ZipCompressionLevelBest];

[stream writeData:abcData];
[stream finishedWriting];

Reading a file from a zip file:

ZipFile *unzipFile= [[ZipFile alloc] initWithFileName:@"test.zip" mode:ZipFileModeUnzip];

[unzipFile goToFirstFileInZip];

ZipReadStream *read= [unzipFile readCurrentFileInZip];
NSMutableData *data= [[NSMutableData alloc] initWithLength:256];
int bytesRead= [read readDataWithBuffer:data];

[read finishedReading];