Hello Sami! Here is LOTS of information regarding applying new lawn seed. https://www.lowes.com/projects/lawn-and-garden/seed-your-lawn/project
When the weather is still cool, seed will germinate the best if you keep it watered.
Buy a good quality seed. Some have a fertilizer in it and a product also to stop the birds from feeding on it.
The BEST time is the fall when grass will still grow but weeds have died back (if you have any in the grass). Now is great, sow the seed and cover with a straw and water daily until you see it get up to good height. Do not mow it until it has filled in thick and is well rooted and established.