Choose an achievable first target
Start with enough to cover one common unexpected expense. Once reached, build towards several months of essential costs if that fits your situation.
Make saving automatic
Transfer a fixed amount shortly after payday. Even a small amount is easier to maintain when the decision does not need to be repeated every month.
Keep it separate but accessible
The money should be easy to reach in a real emergency but not sit in the account used for daily purchases. Decide what counts as an emergency.
Refill it without panic
When you use the fund, it has done its job. Temporarily adjust other goals and rebuild it calmly.