As with all learning processes, it's going to depend upon the student. It will also depend on just how familiar you are with those existing languages, and whether there's a major paradigm shift between languages. For example, someone well-versed in C# and Java might stumble at first when learning a functional language like Lisp, or a logic language such as Prolog, because the entire approach to problem solving is different.
In terms of learning the language, one can pick up the syntax and grammar fairly quickly, either with an online tutorial or a good book; many resources exist for languages which act as "conversion course" material - that is, rather than cover subjects such as "this is a variable", they take the perspective of, "this is how we declare variables in this language".
Of course, learning the language and its associated idioms requires more than just pure syntax; you're going to want to learn the entire platform; the supporting libraries and API, if you want to get anything productive done. For example, learning C# is all well and good, but if you don't bother to learn part of the .NET framework in the process, you'll struggle to do anything really interesting. Fortunately, someone well-grounded in the language basics can usually pick up platform specifics fairly easily, as long as the documentation is reasonable.
In the long term, the best way to get really comfortable with a language and platform is to code a lot in it; several small projects to get used to the various idioms and best practices for different common tasks, and then perhaps one or two medium-sized projects to give you a chance to challenge yourself. Of course, developing true language expertise will take many, many years...but I think I've discussed this before.