How to get started learning Chinese?
Learn Chinese

I could just assume you mean that you want to learn to speak Mandarin Chinese, but I'd like you to take a moment to share what you mean by "learn chinese."  Since it will likely be the hardest thing you've ever tried to do, I'd recommend you consider the following:


Mandarin is the most popular dialect and the official language spoken
throughout China (but many variants exist) 
Do you want to learn to read and write as well? (this can help
comprehension)
Do you have anyone you can practice with or would you need to partner
with someone who speaks the dialect you want to speak? (See italki.com)
Assuming you are not in China, you should Google your local Chinese
community to learn a bit about a "china town" near you (visiting a
local sit down Chinese restaurant and speaking with Chinese staff may
be a good way to get some interactive Chinese - let them know you want to learn, most Chinese people are pretty good about helping language learners practice)


Overview

You will likely want to review music, texts, and conversations. A common method of getting started is use of tourist books/apps/websites that focus on the most important phrases one needs. You can try to immerse yourself or take things very slowly. Eventually you will want to understand spoken Chinese in order to engage in a conversation. Without knowing your budget it would be hard to provide a precise plan. Generally, if you are looking for free help/products then you will be able to find these online by searching (just keep in mind that some of the resources may be hard to navigate). If your budget allows, you can look at buying a book or getting an introductory personal lesson (if you are near a big city or one with a large Chinatown).

Getting Started

Many of the questions/answers on this site actually end up providing good references to online resources. I suggest you start by reviewing this site for references to other online sites that have audio, visual, spoken, and written materials. Here's one such question. I recommend you review each answer and bookmark the websites. Many of the resources are free. You can also do a Google search. A used book on Reading &amp; Writing Chinese can help, see my answer here for a good cheap source. You might also:


Review Tutorials on Youtube
Check out Chinese Music Videos on Youtube (Here's a mix of some
modern Chinese music or some amazing singers from a popular show)
Review iTunes University for Chinese Material (if you have iTunes or
an iProduct, will also work just fine from browser as this example)
Check free mobile apps for your phone
Bookmark many external sites mentioned in answers on this website (Here is a link that holds Mandarin Sounds and Phonetics)
Start collecting language notes (you might try using Google Docs for this)


Books

I believe in getting the right book and would encourage you to look for a book that is well organised. As an example, the book I mentioned earlier for Reading &amp; Writing Chinese, introduces characters in a very logical order (with each character building on the next one). The result of this is that you will learn multiple characters that look similar at points where it is easy to see the relationships between them.

A quick example:

McNaughton &amp; Li (1999), p. 35, presents these characters in sequence:

冂，囗，十， 田，厶 followed on p. 36 by

幺，八，小， 糹，累

The right book can ease the learning experience if well-ordered.

Common Grammar Points

Chinese and English are both basically Subject Verb Object (SVO) languages so you will find many consistencies between the languages. This means one can take a basic sentence and simply replace with a Chinese synonym to have the same meaning. This is of course not always the case (meaning there are many variations) but I want to assure you that learning Mandarin is not only possible but can be easier if you think in grammatical terms.

A quick example:


  
  I am American (person) 
  wǒ shì měi guó rén
  我是美国人
  (more on Mandarin Grammar Word Order and English Sentence Structure)
  


Free Mac OSX Chinese English Language Guide

I have a Mac OSX Guide which details how to setup a Mac OSX system to enable Mandarin, Cantonese, and English speech, Pinyin Conversion, Chinese Writing, and Chinese-English Dictionaries (please check my profile for the links). Sorry that I don't have this for Windows but I've made everything one needs to get started for free. If I get a lot of requests for Windows setup then I'll pull together the material.

Video Demo of MCE Tools 

Final Thoughts

If you need more help, please edit your question further and I can refine this answer. I encourage you to jump right in and enjoy the journey.