It is unusual to grow Forsythia from seed as most of those grown are hybrids and will not 'come true' from seed. They are very easy from cuttings.
If you collect seed, store dry until autumn and sow outside in a tray. You never know!

If you want new plants just stick the stems you prune off after flowering into the ground and leave them for a year. They root very easily with no supervision! I have used them for pea sticks and finished up with new plants!