I'm no expert on Iran's geopolitical strategies nor do I think anyone can accurately predict their response with any real precision, but I do think history (particularly over the past 20-30 years) gives us a bit of a template for how Iran is likely to retaliate.
1. They're going to use proxy forces to preserve plausible deniability. Think Shia militias, Hezbollah, their terrorist apparatus which extends throughout the Middle East, Asia, and even Europe and the Americas, other Shia groups/allies, etc.
2. I think their goal will be to kill Americans -- whether civilian or military.
3. There's not going to be some large-scale conventional attack by uniformed Iranians or a direct military engagement with our military forces. Iran will do what they always do, and what Soleimani was so adept at. They'll arm their proxy forces with additional technology and weaponry and start plotting.
I think these three reasons are why we've continued to strike Shia militias in Iraq today. Some recent news came out from Reuters that the "imminent attacks" that Pompeo and others had publicly mentioned referred to Soleimani's recent planning to escalate attacks by having proxy forces attack US trooped in Iraq and in other areas of the Middle East.
They were arming militias and proxy forces in and around the Middle East (particularly in Iraq) with drones, more advanced precision weaponry, etc because they wanted to draw an American military response in Iraq that would distract people from the recent anti-Iranian protests and increased anti-Iranian sentiment due to Iran's meddling and control of Iraqi political affairs. Supposedly this even included recent planning with Hezbollah to attack US targets in their sphere of interest -- perhaps US diplomats. They always seem to love to target our diplomats and spies in Lebanon.
Although some kind of retaliation could happen at any time, I think it will be a thousand cuts rather than any big event (although you may have some larger attacks mixed in). Kill/kidnap an American citizen here or there. Attacks bases and military personnel with renewed IED/suicide bomber campaigns, although right now they seem to be found of rockets.
Might see a few larger bombings mixed in if they find a few suitable targets where they've scouted well for weaknesses. Hit a diplomatic gathering spot/watering hole or a Western hotel US diplomats or citizens frequently use. Possibly even use a mass shooting style attack instead of a bomb. Potential locations might be places like the UAE, Qatar, Kuwait, Iraq, Lebanon, Saudi Arabia, Turkey, Oman, or even possibly Israel.
I think Iran will be under a lot of pressure to act quickly, so that's why I say the first retaliation might occur anytime now, but I think overall once the first counterpunch has landed they will slow down and this will turn into a sustained campaign very similar to the type they've conducted in the past but on a larger scale, more frequent, longer period of escalation, etc.
Just spitballing here, but Iran's overall strategy has been fairly consistent for a long time. Their tactics change, but the strategy of slowly bleeding and cutting hasn't. Iran has definitely conducted some much larger attacks in the past (Iranian directed or by an Iranian proxy), but I think they'll be careful not to provoke too much at first as they don't want further US action against their interests unless they can manipulate it for a larger strategic purpose.
Wouldn't be shocked to see attacks against an ally -- especially Israel. But who knows? Maybe Iran really loses it over Soleimani and miscalculates themselves into an even bigger confrontation. I think that still remains a possibility because even though the Iranians are typically very rational actors, they're human and make mistakes, have emotions, and sometimes the hardliners rile each other up.