: What are the most common root motions rather than the dominant resolution? I'm studying harmony. Most things seem to be based on the dominant resolution, but how do I get to the V7? What other root motions can I use that

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I take your 'root motion dominant resolution' as V>I. Thus you're asking how to get to that V.

A couple of the most common are II>V and ii>V. Others are IV>V, Io>V and Vo>V. The II and ii having 7ths if you like.

Others are available, and a big factor is what precedes the chord which precedes V (or V7). The piece may be at a cadence where it continues straight back to I after V, or it may be modulating into V, which then effectively becomes the new I.

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I think I understand your question a bit differently from the other answers. It seems to me that you're acknowledging (and rightly so) that the root motion of a descending fifth is very common in music; this is, after all, the famous V–I motion.

So it seems you're asking about other common root motions, no? Here are a few:

Root motion of a descending third is quite common, because it results in common tones between the two chords. Think I–vi, vi–IV, and IV–ii; all three of these progressions share two common tones between the triads.
Ascending third root motion does happen; think of something like I–iii. Although this progression also has two common tones between the chords, it's less common than descending third root motion.
Ascending motion by a step does happen, but if you're writing in the classical style, watch out for part-writing violations. I–ii, iii–IV, IV–V, and V–vi are all examples of this root motion.
Root motion of a descending step is relatively uncommon in the classical style, but it became very common in popular music, especially in things like the Andalusian cadence.
Root motion by tritone is pretty rare and often saved for special effect purposes.

The root motion by fifth you mentioned is the same as motion by fourth, by third is also by sixth, and by second is also by seventh. So the above list should exhaust all possible root motions.

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I think you are asking about resolutions that are not dominant, right?

The second most common one is the Plagal cadence (IV I), witch is broadly used in popular music, being also part of the 4 magic chords.

There are several simple examples here.

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The Bible of traditional harmony is Bach's collection of chorales.
www.amazon.co.uk/Harmonized-Chorales-Johann-Sebastian-Bach/dp/0793525748
Any traditional hymn book comes a close second. Study a few. You'll find plenty of dominant-tonic cadences, and plenty of ways of getting to them.

Here's one. There's a V-I cadence half way through the first line, then a 'V of V' - V one at the end of the line. In functional notation it's I I IV Ib VI IV V I (I use 'b' to indicate a first inversion. There are other ways.) Or C, C, F, C/E, Am, F, G, C in chord symbols.

Note that a lot of popular music doesn't really work this way. Traditional harmony grew out of part-writing, the chords sort of 'just happened'. Pop/rock songs are often written by guitarists, who see chords as seperate entities, and the sequences may owe more to shifting a shape up the fingerboard and thinking 'That sounds good!' than to any particular 'theory'. That's fine too!