Welcome to the site! I'm afraid there isn't exactly one way to rule them all. But there are various phonological rules by which you can guess the roots of a significant number of verbs.
For example, -(i)sk, -nu, and -an are common present suffixes, so cut them off if you want to find the root. The -an- suffix is in the present manthanô (root math-); -nu is in deiknumi (root deik- or dek- or dok-); -sk- is in heuriskô (root heur-). There are various other suffix that aren't part of the root, like the common -eu- and other vowel clusters in pisteuô, dêloô.
Gemination of the final consonant is often due to a present suffix (invisible -y), too. Cf. ballô (< bal-y-ô), root bal-.
The infix -n- is a common in present stems as well. It can be rendered as mu (perhaps also as gamma) due to assimilation with the consonant after it: it is a mu before labials, gamma before velars, I believe. Examples are manthanô, root math-, and lambanô, root lab-.
Reduplication (semi-repetition of the first syllable) can be a present praefix, and is often a perfect suffix. E.g. present didômi, root do-, perfect leluka, root lu-.
Etc. So removing all affixes is often a good thing to try in case you want to go from present stem to root/aorist. Some affixes are used in all classical forms of the verb but not in nouns or other words from the same root, so you might only see the true root outside verbs. Of course the converse is also possible (nominal affixes not present in verbs).
Then there is the phaenomenon of Ablaut: in Proto-Indo-European, which is also Greek's ancestor, many roots had three potential manifestations, 1.) a "zero grade" where nothing is added to the root, e.g. lip, 2.) an "e grade", e.g. leip, and 3.) an o grade, e.g. loip. So you can try removing an e or o when present, or adding one when not present in case you're going from root to present stem. Other examples are peithô, root pith-, and pet-o-mai, root pt- (aorist e-pt-o-mên, perfect pe-pot-ê-mai).
A nice example is ker-an-nu-mi "knead" (as in English ceramic). It has -nu, and it has -an-—or is that really only -n-, since many other forms of the verb have the a without the n (aorist e-kera-sa)? The verb seems to show Ablaut, too, as we have perfect ke-kra-mai. Liquids (m, l, n, r) surrounded by too many consonants are often vocalised (turn into or acquire a vowel sound) in Greek; in Attic-Ionic dialects, this is usually a, so that might be where the a came from in the perfect, which was then perhaps generalised and also used in places where it wasn't 'necessary', as it often happens in language.
I'm sure there are other rules of thumb that apply to some other verbs. But there will be many where you probably can't find a rule that would apply, alas. So you will need to learn all verbs by heart, in theory; but you can save yourself a lot of work by trying these rules of thumb; they are never guaranteed, but I believe they will provide you with a high chance of success for quite few verbs.