How do I do git push with JGit?

The easiest way is to use the JGit Porcelain API:

    Git git = Git.open(localPath); 

    // add remote repo:
    RemoteAddCommand remoteAddCommand = git.remoteAdd();
    remoteAddCommand.setName("origin");
    remoteAddCommand.setUri(new URIish(httpUrl));
    // you can add more settings here if needed
    remoteAddCommand.call();

    // push to remote:
    PushCommand pushCommand = git.push();
    pushCommand.setCredentialsProvider(new UsernamePasswordCredentialsProvider("username", "password"));
    // you can add more settings here if needed
    pushCommand.call();

You will find in org.eclipse.jgit.test all the example you need:

• RemoteconfigTest.java uses Config:

  config.setString("remote", "origin", "pushurl", "short:project.git");
  config.setString("url", "https://server/repos/", "name", "short:");
  RemoteConfig rc = new RemoteConfig(config, "origin");
  assertFalse(rc.getPushURIs().isEmpty());
  assertEquals("short:project.git", rc.getPushURIs().get(0).toASCIIString());
  

• PushCommandTest.java illustrates various push scenario, using RemoteConfig.
  See testTrackingUpdate() for a complete example pushing an tracking a remote branch.
  Extracts:

  String trackingBranch = "refs/remotes/" + remote + "/master";
  RefUpdate trackingBranchRefUpdate = db.updateRef(trackingBranch);
  trackingBranchRefUpdate.setNewObjectId(commit1.getId());
  trackingBranchRefUpdate.update();
  
  URIish uri = new URIish(db2.getDirectory().toURI().toURL());
  remoteConfig.addURI(uri);
  remoteConfig.addFetchRefSpec(new RefSpec("+refs/heads/*:refs/remotes/"
      + remote + "/*"));
  remoteConfig.update(config);
  config.save();
  
  
  RevCommit commit2 = git.commit().setMessage("Commit to push").call();
  
  RefSpec spec = new RefSpec(branch + ":" + branch);
  Iterable<PushResult> resultIterable = git.push().setRemote(remote)
      .setRefSpecs(spec).call();