There are numerous ways that God can intervene in our lives. The following are a few; my experience with each is summarized, as well.
1) The Lord intervenes directly. In short, he commands the elements to obey, and they do.
I have had that sort of experience - once with the actual elements.
2) He sends heavenly messengers to help without making their presence known.
I’m not sure how I would know if that had happened, since it would be done “without making their presence known”. Just saying. *grin*
3) The Lord inspires someone at the right time, and sends inspiration so that someone can help someone else.
I have had this experience (miraculously) in the past, perhaps most obviously driving late one Saturday night to get my son from college. The “coincidences” it took to have my "broken" car fixed so quickly were so numerous I choose to chalk it up to intervention.
4) Someone is inspired as to what she needs to do to fix a problem. This inspiration goes beyond her current knowledge.
I have had this experience many times in various situations, especially with blessings.
5) Someone feels the spirit to fix what he is capable of making based on his knowledge.
This has happened to me many times.
I hope we teach our children that God can and will intervene sometimes (directly and miraculously), but that the general rule for most people appears to be inspiration to self or others. On the other hand, I also know members in countries or areas where there is little or no chance of receiving help from others (like in medical emergencies), and the obviously miraculous seems to occur there much more often than here. I don’t know if that is due to differing levels of faith or differing levels of need for intervention, but I like to think it is the latter - that God will help more where more help truly is needed.