If your monitor has DVI, you can use an HDMI-DVI cable. HDMI and DVI are essentially the same thing with a different connector. The main difference is that HDMI can carry both audio and video while DVI is only video. However, the audio isn't lost if you go from HDMI to DVI to HDMI again via adapter cables, so the DVI connector is technically capable of audio as well. In fact, some newer graphics cards allow their DVI ports to function as HDMI ports and output audio and video.
VGA, on the other hand, is an old type of connector. It is still good quality, but is best for CRT's and not LCD's. DVI connectors have the ability of outputting a VGA signal, essentially acting as VGA ports, and using a connector adapter to change the DVI port into a VGA port so you can connect a monitor. However, HDMI does not have this analog mode, so you can't go from HDMI to DVI to VGA because even though the connectors fit, the HDMI laptop won't be able to output an analog signal. Many HDMI laptops also include a VGA port (my laptop has S-Video (7-pin with composite/component output as well), VGA, HDMI, and the built in screen, a total of 4 video outputs) to make up for the lack of a compatible DVI port.
If you don't have a VGA port, your only option will be an active converter. This device will decode the digital signal into an analog signal for your monitor. It will also be quite expensive, as signal conversion isn't exactly simple.