Hi, I have a vps server and wanted to run a voice over internet telephone system can I do it over the internet using a vps or defecated server. If so how.

You'll need SIP trunking (and a SIP trunking provider) or some way to connect your system back the PSTN (public switched telephone network), assuming you want to make calls back to phones not on your voip system. You'll also need low latency connections, and a reliable connection on the client side.

As to how, people write books on that topic, I'd suggest you read a few.

Actually "low latency" is not that important, as long as it is not "too high latency". Jitter and packet loss are much more important than latency.
@markgrannum18 search for asterisk - it is a free opensource IP PBX software. Yes it can be run in a VPS with great success, as long as the VPS (and the underlying hardware node) are not overloaded, and as long as the network is good and stable (i.e. no packet loss, no jitter).

You can use a VPS and install PBX in a Flash also known as PIAF. So providers will also install it for your on the fly.

Preferably you'd run end to end QOS, this will help with jitter, packet loss, and latency. What kind of router and connection do you have on the client end? If you're using a modem-router forget about it until you invest in a proper router (like a cisco, or a cheap but reliable machine using linux as a router and sip proxy), and have the skill to troubleshot difficult networking issues. Voip on the cheap - been there, done that, it was a nightmare.

Your plan might be workable if you're willing to invest a lot of time and a reasonable amount of money in it, and you like studying, or are already an expert at linux administration and networking.

If you don't know what's involved, months of work, testing, and study, equipment, sip trunks, and at least a high quality (Xen or VMWare) VPS reasonably close to you. If you like the challenge, have the money for testing and equipment, skill, and the time, to invest in making the system work properly, and/or your phones aren't mission critical, go for it, otherwise, your hidden costs will pile up until you realize you're throwing good money after bad.

Preferably you'd run end to end QOS, this will help with jitter, packet loss, and latency. What kind of router and connection do you have on the client end? If you're using a modem-router forget about it until you invest in a proper router (like a cisco, or a cheap but reliable machine using linux as a router and sip proxy), and have the skill to troubleshot difficult networking issues. Voip on the cheap - been there, done that, it was a nightmare.

Your plan might be workable if you're willing to invest a lot of time and a reasonable amount of money in it, and you like studying, or are already an expert at linux administration and networking.

If you don't know what's involved, months of work, testing, and study, equipment, sip trunks, and at least a high quality (Xen or VMWare) VPS reasonably close to you. If you like the challenge, have the money for testing and equipment, skill, and the time, to invest in making the system work properly, and/or your phones aren't mission critical, go for it, otherwise, your hidden costs will pile up until you realize you're throwing good money after bad.

I have to disagree with some of this.

VOIP can work very well with domestic routers (although some of them are not suited to VOIP due to their handling of SIP traffic) and GUIs make configuring fairly straight forward.

If you've got a stable internet connection with no packet loss and little jitter that's not over utilized you can get great results. I have customers doing this every day to prove that.

Entry level costs are minimal compared to a traditional PBX so why not give it a go.

Maybe one or two voip phones would work behind a consumer router, especially a half decent consumer router, but modem-routers aren't half decent consumer routers, they're the cheapest of the cheap and real worthless pieces of crap. They'll get two or three working fine, but crap out after that.

If the provider's system is managed for voip, and comes with sip trunks, it would make things a lot easier.

Have a play with asterisknow or trixbox to get the hang of it if you are new. Alternatively, there are loads of 'how-tos' on the net.

VoIP is not easy to master and consumer kit generally is the toughest part to master (if you can avoid them, all the better!).
Installed Asterisk and FreePBX and with a bit of time, effort and hopefully not to many tears you may get it up and working. :)