This happens quite a lot with clients new to AdWords. There are many reasons why your AdWords text ads are not being shown. Here are some common reasons and what you can do to check for problems.
Payment and budget type issues would be the main cause. Waiting for a payment to be processed can vary. The time required will depend on which payment option you selected. For example, if you have opted for Pre-Pay by direct credit then it can take up to 3 days for the banks to process payments. If the credit card or debit card is rejected, the ads are suspended until the account is paid. At the campaign level there can be issues. Your campaign requires $20 a day for your ads to show all day, and your budget is $10, then your ads will only be shown for 50% of the searches for your keyword term. You receive a lot of clicks earlier in the day meaning your budget ran out, so your ad won't be shown at all in the evening.
Ads Under Review. It can take take up to 5 days for ads to be reviewed and approved. Remember you must follow the ad guidelines. Note that if you change an ad, Google reconsiders it and treats it as a new ad.
Any time you want to test for ad, or keyword delivery problems go to the Keywords tab of your campaign and find the Status column. There is a little "talk balloon" graphic on the line for each keyword. If you hover your cursor over the graphic, this tool will run an instant diagnostic on that specific keyword, testing quality score, relevance, and landing page load times. If there's a specific problem this tool can suggest what it might be. From there you can go to the Ads Diagnostic Tool.
The Ads Diagnostic Tool can also be accessed by the Opportunities tab. Put in the information for your campaign, making sure to include a search location that is inside your campaign's geotargeted area, and language and run it. It will test all of your campaign keywords to see if they're active to trigger ads at that moment. If there's a problem, this tool can suggest what it might be and point you in the right direction.