Not long, if I remember correctly. But I was already familiar with programming and I had an older brother that had been working with SQL for years telling what I needed to study, so it didn't take long at all. SQL is a lot different from regular programming languages because it's declarative, meaning you tell it what to do, and it does it for you, in opposed to procedural languages (Java, C, C++, C#, Objective C, etc.) where you have to build a program step by step. But still, SQL has some of the basic constructs found in all languages (data types, functions, some OO principles, etc.) so your best bet is to get familiar with those terms.
Here is a pretty good resource you can use to get familiar with SQL and database programming (I suggest following along doing everything by hand). This is an online tutorial used by students at Nanyang Technical University (one of the best Tech schools in the WORLD)...
How to Install (on Windows, Macs, Ubuntu) and Get Started with SQL
MySQL by Examples for Beginners
A Quick-Start Tutorial on Relational Database Design
Database Programming: An Intermediate MySQL Tutorial - Scripting, Data Types, Examples
MySQL Sample Databases
Go through those links, learn and complete everything and you should have a pretty solid foundation in SQL and database proprgamming and design. Also, know that ALL websites and 95% of applications is running with some sort of database as its backend. Last, I can't say how quick you'll be able to grasp these concepts because it's totally dependant upon you, how much you study, and how much practice you putting in. Good luck.
EDIT: Oh, and for an FYI, SQL is the ONLY language that I can say without a shadow of a doubt will still be around and kicking 20 years from now. You have concepts like NoSQL trying to get started but SQL is still running strong on about 95% of backend databases. That shyt ain't going no where anytime soon so invested time in SQL is a pretty good investment of time.