Via NetBeans File Systems API, which provides FileUtil.copy below, which means a dependency on NetBeans Utilities API:

private void unzipEpubFile(String folder, File file) throws IOException {
    final AtomicBoolean canceled = new AtomicBoolean();
    //define and start progress bar here...
//        ProgressHandle handle = 
//                ProgressHandleFactory.createHandle(
//                        Bundle.MSG_unpacking(zip.getName()), 
//                        new Cancellable() {
//            @Override
//            public boolean cancel() {
//                return canceled.compareAndSet(false, true);
//            }
//        });
    //then unzip 'file' into 'root":
    try {
        List folders = new ArrayList<>();
        try (InputStream is = new FileInputStream(file)) {
            ZipInputStream zis = new ZipInputStream(is);
            ZipEntry entry;
            while ((entry = zis.getNextEntry()) != null) {
                if (canceled.get()) {
                    return;
                }
                String n = entry.getName();
                File f = new File(folder, n);
                if (n.endsWith("/")) {
                    if (!f.isDirectory()) {
                        if (!f.mkdirs()) {
                            throw new IOException("could not make " + f);
                        }
                        if (entry.getTime() > 0) {
                            if (!f.setLastModified(entry.getTime())) {
                                // oh well
                            }
                        }
                    }
                    folders.add(f);
                } else {
                    //handle.progress(Bundle.MSG_creating(n));
                    File p = f.getParentFile();
                    if (!p.isDirectory() && !p.mkdirs()) {
                        throw new IOException("could not make " + p);
                    }
                    try (OutputStream os = new FileOutputStream(f)) {
                        FileUtil.copy(zis, os);
                    }
                    if (entry.getTime() > 0) {
                        if (!f.setLastModified(entry.getTime())) {
                            // oh well
                        }
                    }
                }
            }
        }
        //handle.switchToDeterminate(folders.size());
        if (canceled.get()) {
        }
    } finally {
        //stop progress bar
    }
}

Mostly from NetBeans IDE sources for working with projects and ZIP files.