In this example, I'm using the ProQuest Central database. The search here was for how does the American Cancer Society Spend Money. I used American Cancer Society in double quotes and spend and money. I checked the full text box underneath the search box, so the results will be full articles.
On the left, there are a number of ways to limit. Besides date range, you can also limit to publication type, specific publication, location, etc. Just choose what meets your needs.
In the case of ProQuest, You can limit by date range with the sliders on the left or by typing in a date range where it says enter a date range.