how to get my website showing in google and other search engines

is this free?

Yes.  Pretty much only the scammers charge for signing up with search engines.  Bing has something similar that is also free.  http://www.bing.com/toolbox/webmaster

and will this mean when someone searches my name it will come up in the first few pages

Before you assume that you are not listed .. have you tried to check if the URL is on the Google indexes?
In the google search box .. enter the domain name as follows (where yourorganisation.com is the domain name of the non-profit)

site:yourorganisation.com

you can also type

link:yourorganisation.com

This will show you if Google has found any other websites which link to your domain.

If can often happen that one or more pages on the website ARE on the Google index but due to the design, coding or cache of the page that Google has taken it is not ranking highly for the search term you are using.

Creating a sitemap.xml file and registering for FREE with Google Analytics and Google Webmaster Tools .. including the analytics code in the website header will definitely improve how often and in how much detail Google will visit the site.

To expand on @eoinosullivan's example, the search term "donate to charity" on Google returns...

About 172,000,000 results

and you would be 172,000,000 and 1.

While it is good to be found, the way to do that these days is make sure your location is mentioned in your content along with any 'prominent people' and causes and activities associated with your organization.  Try to get your site mentioned by others and advertise where it's appropriate, especially if it's free.  Don't pass up chances to promote yourself.  Get your events on local calendars.

all i need is that when people search for the company name ie companyxyz in google it shows up

Depends on the actual companyxyz name and how common it is  .. if you use my link:companyxyz.com in Google and you know that the website is in the Google index but it does not appear when you enter companyxyz in the search box on the first few pages of the search results .. then you need to add google analytics, use the webmaster tools and do a bit of work to improve the visibilty of the site.

Unless you tell us the name of the company and the url .. we cannot be more specific than that.

Have you searched for "the company name" in Google?  ACME, the fictional company, returns About 54,800,000 results.  Very few companies have unique names.  I have websites that have almost unique names... because I searched Google for them before I got them.

my is a unique name

Can you confirm if you've checked on google using the link: parameter?  Is the domain listed on Google or not?

mine is a unique name

Only if Google says it is.  Go search for it.

There are many free directory sites that will list your site. An older site about local web promotion is here.
http://seattlewebpromotion.weebly.com/local-web-promotion.html

I would be very, very careful about attempting to do that.  Those "free directory" sites are not always seen as quality backlinks and can do more harm than good.

A lot has changed since 2011, David.  And you really should disclose you are the author at the above link

There are several SEO | local web promotion newsletters I read.

http://webmarketingtoday.com/
http://www.brickmarketing.com/
http://searchenginewatch.com

if i want it just to show up when someone searches the company name what do i need

LOL ... save endangered icelandic lemmings returns 1,330,000 pages ... go figure.

There are only three things certain about search.



However the rules Google uses and changes when ever it pleases are a secet and all you will ever get are clues and suggestions.  If you don't follow the suggestions then Google won't like you.

You may find it good to abbreviate Google to God in any correspondence with them if you want them to like you.

Cd&