Like the above poster said, a lot of what you can do will depend upon your income.
That said, everyone should save 6-12 months worth of post-tax income as fast as they can. This gives a little cushion should something happen and you need to find a job. On top of that, you need something to dip into for emergencies that don't involve unemployment, though worst case, you can use the 6-12mo fund if you replenish it. In addition, everyone should put aside at least 10% of their income for retirement (ideally) or split between a retirement and rainy day fund.
Obviously, those of us who make less and live paycheck to paycheck will find it more difficult. Those just starting out who aren't used to a full-time income will least miss automatically putting aside 10-15% of their paycheck and will be starting a great habit. No matter what you make, if you are used to spending everything, it will be tough to get used to limiting your spending and putting that money aside. Still, the future is coming for all of us, things do happen, eventually, even if we don't plan to retire, our health may not give us a choice. Put aside as much as you can and be prepared.