The first thing to understand is that signing is a language, and as such, it is much easier to learn when you use it regularly. It is also much easier to learn with a more fluent guide to help you. Look around the community for resources through the League for the Deaf & Hard of Hearing, or community classes through a local community college or YMCA. Consider why you want to learn. Is there someone who you want to sign with? Ask them to help you. Do you want to teach your infant 'baby sign?' Contact local women and children organizations or a local midwifery group that may have community resources.
Think about simple words that would be most helpful for you. If you intend to teach your infant to sign, basic one-word phrases will suffice for you as well. If you intend to communicate through sign, you will eventually need to know how to string together words into statements. Make a list of these words. For infants (and perhaps adults as well), think about the basics: bathroom, more, juice (or milk or water or drink), sorry, please, thank you, happy, sad, silly, tired, yes, and no. If you are looking to use sign as a supplement for students who are learning sight words, your list may look a little different. Either way, know what words are the highest priority to learn.
Use your reliable models: books from the local library, dictionaries for sign language, friends who sign, and trustworthy web sites (see attached) to acquire a few words. Use them regularly to ensure you maintain them. Ask others for feedback.
Once you are comfortable with your first few words, begin to add others. Think about ways to make statements with your words. What other terms do you need to be able to say. For example, if you know 'happy' what would you want to say that you would need to find out. Terms like 'I feel...', 'Are you', or 'She is' might be helpful.