Be intentional. Set a budget and stick to it. If you don't know how to set a budget, there are a lot of places to get free resources, or better yet, to take a class. Financial Peace University or Crown Financial Ministries are great places to start.
These places give you guidelines as to how much you should be budgeting for different items such as your home, food, clothes and even entertainment. Of course you can't budget for income you don't have so that's a consideration as well. They also give great tips on how to get rid of debt and start saving.
If you try to cut corners in what you spend, but never intentionally put some into savings, it will be much harder to save. You can always start by putting a percentage of whatever you make directly into a separate savings account, but if you're not able to put some into savings and still make your bills, then there are some serious considerations you need to look into in order to prioritize your spending or reconsider your lifestyle and/or job.
Saving isn't easy, but it is possible. In a society filled with instant gratification and a "buy now pay later" attitude, you really need to block out the hype and the media's attempt to get you to buy everything and live above your means. You can do it.