We have all heard the saying "You only have one chance to make a first impression". I am not completely convinced that it represents an absolute truth, but it seems a reasonable guideline to keep in mind when preparing to network with a potential contact for a job lead. Notwithstanding all the factors such as being appropriate in attire and deportment (since visual elements contribute significantly to the experience) the actual words we use to introduce ourselves are worthy of some serious consideration.  

Introduce your introduction. It's helpful to set the stage by saying something like this... I would like to give you a short overview of my background and my career goals and I hope you will offer your perspective.  Naturally, I will be happy to answer any questions you might have.

BRIEFLY summarize your business background and desired next steps. My career has focused on two areas; technology and finance, and my goal is to use my expertise in these disciplines to become Chief Operating Officer for a global corporation.

Add context. My most successful roles have been in companies with dynamic, fast-paced environments where the strategy includes combining innovation with practical discipline. I'm most interested in sectors such a transportation, telecommunication and commercial construction.

Ask for reactions. Based on what I've just mentioned, what questions or comments do you have?  I value your perspective and guidance on companies or individuals who might be good contacts to talk with about a possible fit with these sectors. 

Do not belabor the reason for leaving your former employer.  If ever there were a time to apply the "short and sweet" rule, this is it. Be truthful and brief by stating something similar to this... There was a reduction in force due to (e.g.) a merger, an acquisition, a downtrend in the business, off-shoring, management change, change in business model, etc.  Quickly move to a positive view of the future with a statement such as ... It was a great run, and now I'm eager to transfer my skills to another firm.

It is not feasible to script the entire conversation, so simply listen carefully to comments and questions and pursue each one to the fullest extent possible in the moment. When your contact shows signs that the meeting is coming to conclusion, ask if it will be alright for you to contact him/her again once you have thought about what you learned from the chat. Be certain to extend your sincere thanks for the meeting and offer to help if there is anything you can do to return the favor.

Hopefully, everyone will want to learn more about you and feel comfortable guiding you to possible job leads, in part due to the great first impression you make. Good luck!