The seed pods should be brown and just beginning to crack open, and the seeds inside will be brown. Save them in a paper bag, somewhere cool, dry and dark till next spring. Open the pods.
Keep nipping off the dead flowers to get new ones once you have decided you have enough seeds.
If you soak them in warm water before sowing, they will germinate quicker.
Keeping in mind that seeds one buy to plant in the spring are derived from hybrid plants… bred from various varieties for certain aspects… the seeds you harvest may or may not produce the same plant...
The seeds you buy will be disease free .. the seeds you harvest from this years peas are from an unknown source and their heritage unknown as Clanad has alrwady pointed out.
Why bother ... next year you may sow them and they may or may not give you problems. Why take the chance to save yourself 99p.
Compost the old plant, seeds and all. Otherwise next year you wil be asking ... why are my sweet peas not germinating.
I grew sweet peas from seed I'd saved last year. I sowed them in a bigger pot than those you buy (so the roots wouldn't grow so tangled) around March time and planted them in May (I think) while they were still quite small. They've tuned out to be the strongest healthiest ones I've had for years. The only downside is they're all either purple or mauve but the fragrance is lovely. Have a go. :)