OK, let's address the mechanics of the matter, not what you tell the PCs;
Future Predictions: simply use the shifts of the ritual for a Scholarship or Lore or other Knowledge-based skill roll to predict future events. You aren't predicting the exact events here - the future is always in motion - but you are using the skill roll to make an "educated guess" as to how the future will pan out. For example, with resources rolls of +5, the best financial advisors in the world predict the economic movements of the market. With a magical resources roll of +20, which is orders of magnitude higher since the progression is nonlinear, you'd make such an accurate "educated guess" to be actually predicting the future of the economy. Similarly, Scholarship and Contacts rolls of +4 to +5 would allow a world-class politician or businessman to find out information via research or his allies and interpret it to expect imminent political events. With such rolls in the +20 region, your magically enhanced "educated guess" is accurate enough to actually predict far-off events. Contacts of +20 alone could allow you to contact, instead of a human information broker, a mighty supernatural spirit that lives in the future or a greater demon that knows what is being planned worldwide.
Finding Information: a +5 investigation or scholarship or lore roll is average for a world-class human. A +11 roll is the best possible roll for a world-class human that is also helped along by Fate. A ritual giving you a +20 roll is far more powerful than that. Not only you are going to find orders of magnitude more info on the subject than the best effort of the best humans in the world, you are going to find it in the one scene it takes to cast the ritual, not after weeks or even months of research on a subject.
Foresight: the above methods, while giving really powerful results already, are not definite predictions. Foresight is delving into chronomancy to apply chronomancy-related aspects for a specific situation. With a 4-shift chronomancy maneuver, you can apply a sticky aspect to yourself like "Deja Vu" or "I know what happens now". This aspect represents a limited knowledge of the actual future - a real prophesy you forced via chronomancy. You can use this knowledge once to boost any action related to said prophesy by +2 (tagging the aspect) but since that changes the future, you'll keep the knowledge but using it more is harder and harder (you must pay fate points to invoke it again). Aspects like that can be compelled, such as in trying to avert the event you inadvertedly cause it instead, or prophesy misinterpretation in other ways. To gain deeper insight of the future, just add more aspects with a bigger spell or multiple spells - a big spell reflects deeper knowledge such as a major prophesy you gain via major chronomancy once while multiple spells reflect a smaller but constant ability to peer into the future.
Major Prophesies: this is the Divination equivalent of pulling meteors out of the sky or killing entire nations with Disruption magic. Consider how much knowledge, how much information and how much foresight a Divination with thousands of shifts can give. Don't mess with those.
Swimming against the currents of time: Bad idea. But possible. Simply generate enough shifts to take yourself out without concession for alteration of your own timeline (since you cannot naturally conceed that your timeline is altered - it's a forced effect) and then add shifts for duration for how far ahead or behind you want to travel. How you use the time-travel is up to you. I'd suggest running real fast; the Gatekeeper is badass.
