No license allows you to take copyright ownership away from an author, all authors of the source code should always be attributed. As you contribute to the project, your name can be added to the list of authors and will be included along with the others.
Some source files contain a list of contributor names at the top of each file with the license. Some projects maintain a list of contributors separate from the code, this may be in a specific file or part of the documentation. After contributing, your name can be added using whichever method is used by the project. In either case, it is common to use the version control software to record who contributed which specific part of a file.
If you are merging a portion of an open source project into your own project, then the original authors names and licenses must stay intact. To comply with licensing terms, you may need to add some documentation stating -
Portions of the project have been copied from projectX and is copyrighted by yyyy under the terms of the zzz license.