There are a number of ways of tackling this. None of them "the best way" and all of them with problems in the short term or the long term. The very first thing to say is that multi lingual sites are not easy, translators and lovely people but hard to work with and most programmers see the problem as a technical one only. There is also another dimension, outside the scope of this answer, as to whether you are translating or localising. This involves looking at the target audiences cultural mores and then tailoring language, style, layout, colour, typeface etc., to that culture. Finally do not use MT, Machine Translation, for anything serious or if it needs to be accurate and when acquiring translators ensure that they are translating from a foreign language into their native language which means that they understand all the nuances of the target language.
Right. Solutions. On the basis that you do not want to rewrite the site then simply clone the site you have and translate the copies to the target language. Assuming the code base is stable you can use a VCS to manage any code changes. You can tweak individual parts of the site to fit the target language, for example French text is on average 30% larger than the equivalent English text so using one site to deliver this means you may (will) have formatting problems and need to swap a different css file in and out depending on the language. It might seem a clunky way to do it but then how long are the sites going to exist? The management overhead of doing it this way may well be less than other options.
Second way without rebuilding. Replace all content in the current site with tags and then put the different language in file or db tables, sniff the users desired language (do you have registered users who can make a preference or do you want to get the browser language tag, or is it going to be URL dot-com dot-fr, dot-de that make the choice) and then replace the tags with the target language. Then you need to address the sizing issues and the image issues separately. This solution is in effect when frameworks like Symfony and Zend do to implement l10n.
Then you could rebuild with a framework or with gettext and and possibly have a cleaner solution but remember frameworks were designed to solve other problems, not translation and the translation component has come into the framework as partial solution not the full one.
The big problem with all the solutions is ongoing maintenance. Because not not only do you have a code base but also multiple language bases to maintain. Unless you all in one solution is really clever and effective then to ongoing task will be difficult.