I think this very much depends on the idea. There's no formula for finishing ideas. If you know some theory, you can start building chord progressions from the key the riffs are in, or writing other riffs in the key. You can come up with a vocal over the riffs, then see what type of other song sections that inspires. If you don't have any ideas for riffs to play under those vocal ideas, just mute scratch a rhythm that fits, and see what comes along. In my experience, cutting and pasting riff ideas together typically doesn't work too well. Which is not to say that it can't, in fact I'm sure that if you have enough riffs you're bound to have a few that can lead into each other. You might try changing them into the same key, or adjacent keys, and see if that works.
But, at the same time, don't get wrapped up in "making things fit," in a theoretical sense. You don't want to develop a craft that keeps you inside a box. The above are just ideas to hopefully get started making ideas adhere to each other. Take a completely different approach too: listen to you riffs and pick a few that have similar moods, play them one after another, build adjacent sections from them, edit them, improvise over them, turn them head over heels until they spin the way you want them to.
Most importantly, stop asking how and just do it. Writing is not an emotionally easy process. You pour a lot into songs, and as you develop your craft you're disappointed with the return on investment. What's worse, you feel like you're short-changing your inspiration by writing songs that don't do them justice. It would be easy if you could treat every song as an exercise, but of course, with no emotional investment, you're destined to turn out trite garbage. Sad thing is, you need to churn out some bad-to-mediocre before you turn out good. Don't be afraid of it. Take risks, write all you can.