This can take anything from a month (that would be fast) to six months, though a year is not unheard of. I'd expect it to be three or four months. If they decide it can be accepted, we have to revise the manuscript according to the reviewers comments, or explain clearly why we think a suggested change is unnecessary or harmful. The revisions can range from spelling errors, up to redoing the whole model from the ground up, running new sets of simulations or completely change the way we analyse our data. Our changes may be submitted back to the reviewer for further comment if the editor thinks it's needed.
If the editor or reviewers think the paper is not acceptable, or if we don't think the required revisions fit the paper we want to publish, then we give up on that journal. We'll decide on a different journal, rewrite the paper to fit that journal, and submit it again. All in all, six months to a year from first submission to publication would be quite normal. Three months is fast; expect a year and a half to two years if you have to resubmit the paper.
All well and good — except that our project ends next March. We lose access to the cluster computer we've been using for our simulations, and I no longer have a job. We might come to the point where we're asked to do a new set of simulations for the paper and we simply can't: we no longer have the computing power, and I might not even have a science-related job any more so I may have little or no time to work on the model or the paper.
It won't come to that, hopefully. Even if the project ends, we could probably ask for a little computing time to finish the project. And if I find a research-related job it's accepted practice to spend some time finishing up things from your previous projects. Time will tell, as always.