The upgrade from 4.3.3 to 4.3.4 is seamless; I haven't encountered any issue yet after upgrading over 100 systems, whether search head, indexer, or forwarder. The specific steps to upgrade your system depends upon the OS you're using and whether or not you're using native packages (RPM, .deb) etc on the Unix platforms.
However, the basic gist is: download 4.3.4, either use native tools like 'rpm -U' or just click the (Windows / Mac) installer. The first time you start the new Splunk, it will ask you to re-confirm the license, and ask whether you want to migrate your existing configuration. This doesn't touch your indexed data. It will all be present after the upgrade.
You might also consider "accepting" answers that work for you, so that others with the same problem can know whether the solution is a good one.