I'm wondering if you want to plant flowers or veggies or both.* Some of this info, such as your hardiness zone, is more helpful for flowers, shrubs and trees, but most of it applies to all phases of gardening.
It will be helpful to you to know your plant hardiness zone. To find your zone, here's a zip code zone finder.
Here's one that shows a map.
Some other things that are handy for new gardeners to know:
An annual grows from seed, flowers and sets seed and dies in one year.
A perennial will sprout from seed, by runners, offshoots, bulbs or by propagating itself by rooting along the stems. It will usually only form green growth the first year while developing a strong root system (for some plants it might do this for 2 or more years) and will live for many years, even after setting seed it will resprout from the root system.
A biennial will grow from seed the first year and grow only green growth while developing roots. The second year it will flower, set seed and die.
As a new gardener (often called a newbie), the most important advise I always give is to pay attention to the soil. Healthy soil will lead to healthier plants that will more easily be able to deal with drought and pests. To do this you need to add lots of organic matter to the soil and mix in. The best organic matter is compost. You can make your own or purchase it in bulk or by the bag. A 3" or 4" layer on top of a new bed is a good place to start. Always mulch the beds after planting and once a year with organic mulch that will retain moisture, help keep soil temps even, keep weeds at bay and help to enrich the soil. Organic mulches like shredded wood mulch, leaf mold (shredded and rotted leaves), pine straw (just pine needles) are good ones. Compost can also be used as a mulch and the worms will bring it down and mix it for you over time.
Bugs are necessary to pollinate and even clean plants (ex: peonies always have ants on them and keep other bad bugs away). Don't get out the pesticides when you see a bug. Usually there is a good bug predator for most bad bugs. Know thine enemy. There are sites where you can look up which bug is which.
The right plant for the right place is also very important. You don't want to put a plant that needs good drainage and wants full sun in a moist or wet shady place. Remember that full sun is 6 hours or more, part shade is 4 to 6 hours and shade is 2 hours or less. When in doubt and you can't get an answer, contact your local extension service for answers.
Go to the library and look at books on gardening. Many have a plant encyclopedia in the back to help you identify plants and learn their growing needs. There's lots on the web too. Read through lots of posts on forums and try and learn from other gardeners.** When you register at a forum it's best to add your state and hardiness zone to your location so other gardeners won't have to ask you when you have questions that relate to where you live.
You can research plants at http://www.google.com/* It's best to use the Latin or botanical name, but if you don't have it you can search with the common name and when you find the botanical name you can use that to get more info. You can even click on 'Images' at google and often get photos as well. Another way to search is with quotes and a plus sign like this:
*Arizona + "invasive plant"
There are many sites with info on pruning and how to plant trees and shrubs.* There are also sites about native plants and their value, especially for a new gardener.* Native plants tend to be more resistant to pests and diseases and are usually more carefree.
If you would like sites for any of the topics I've mentioned or need more specific info, feel free to ask.* I'd like to know if you want flowers or veggies as I have some sites on gardening in Arizona and garden design.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.