In English, transforming an adjective into an adverb is fairly easy.
adjective adverb
slow -> slowly
French is a bit different, but just as easy if you follow a certain rule of thumb, but as with any language methinks, there are exceptions. This rule covers many adverbs actually, so it works quite nicely.
First Rule
1. Determine whether the adjective ends with a vowel or not.
lent (slow) -- no vowel
2. Since it does not end with a vowel, you need to add one and to do that, you need to convert it to its feminine form.
lent -> lente
3. Now that it has a vowel, all you really have to do is add -ment to it, which is almost the same as the -ly in English adverbs.
lent -> lentement (slowly)
Second Rule
The second rule is that all adjectives ending with -ent do not obey the first rule and there is a reason why I picked "lent" in the first rule. Read on.
1. If an adjective ends with -nt, then to convert it to its adverbial form, we must subtract the -nt ending.
patient -> patie
2. Now you need to add -mment ending to the remaining part of the adjective.
patiemment (patiently)
And there you have it. Recall the 'lent' example. The reason why you cannot apply the second rule to 'lent' is because you would modify almost the entire word if you applied it to the second rule. 'lent' and 'lemment' wouldn't be the same word anymore.
Of course, there are other exceptions and you should be aware of them if you want o pursue French. For example, 'profond' is the adjective, 'profonde' is the feminine form, but 'profondément' is the adverb.
Remember also that if an adjective already has a vowel at the end, you can go straight to the step where you add -ment. For example:
poétique (poetic) -> poétiquement (poetically)
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