Verbs in languages?

You're title's a bit vague, considering how focused your question is!

This is gonna be a bit painful (being Arabic grammar and all that), sorry in advance! I'm gonna start with the roots and radical of a word because it will help the rest make more sense. "Root" and "radical" actually have the same meaning when referring to verbs and words in Arabic. Most Arabic words and verbs are formed from three letters called "root" or "radical" to which other letters are added, following a variety of patterns, called "forms" (there are ten common forms plus a few more that are very rare) when referring to verbs-related patterns.

Words : root + pattern
Verb : root + form

While this make it all a bit of a faff to learn, it also helps you greatly as you will then be able to recognise the patterns and forms and meanings associated to them, which means that if you know the root, but not the word, you can work it out most of the time. If I take the root ك - ت - ب for example, which refers to things related to writing, you can follow a variety of patterns to turn it into different words :

مكتبة means library
كاتب is a writer
كتاب is a book, etc.

You'll notice that you always find these three letters in all the above words, and in the same order, but the other letters incorporated may vary. The same applies for verb, except it doesn't change the meaning of the verb as much as it changes its use in a sentence. It will still be a verb, but you can make it causative, reflexive, etc. Each form has a specific function, and you should pay particular care when learning them. There's a good page on them here, and for the sake of simplicity, I'll copy a few examples in this thread. Remember that the model used for verbs is فعل so you'll find the examples below giving you the form using this root.

خرج - to leave, go out

Form 2 - فعّل (fa33ala)
Built on form 1 by doubling the middle radical of the form 1 verb (adding a shadda to it)
Often is a causative version of the form 1 verb
خرج means "to go out"; خرّج means "to make (s.o.) go out; to graduate (s.o.)"

Form 4 - أفعل (af3ala)
Built on form 1 by prefixing an alif to the form 1 verb and putting a sukuun over the first radical
Similar to form 2 in that it is usually a causative version of the form 1 verb
خرج means "to go out"; خرّج means "to graduate (s.o.)"; أخرج means "to expel, to evict; to produce"

Regular sound verbs are "normal" verbs, in that they are made of a three-letter root and follow forms regularly. Note that if one of these three letters is a long vowel (و or ي), the verb will be irregular. Geminated verbs are also called doubled verbs, and the term simply means that two of the three letters in the root are the same (the second and third, in fact). You will also find hamzated verbs (one of the root letter is a hamza) and quadriliteral verbs (which has four rather than three root letters).

Examples of geminated verbs would include يَظْنّ (s/he believes/thinks) whose root is ظ - ن - ن and where a shadda was added on top of the first ن to indicated that this was a doubled verb.

As for perfect and imperfect are aspects of a verb, and are probably more commonly referred to as past and present tense. My grammar book gives a great explanation:

"Tense focuses on the point in the timeline at which the action occurs, whereas aspect is focused on the action itself - whether it is complete or not."

Arabic is thankfully quite simple in that sense (aspects in Russian are a right bitch) so you can get away with interchanging aspects and tenses without causing confusion, as perfect generally refers to a completed action, whereas imperfect refers to an action that's starting or is ongoing or yet to be completed.

Finally, the moods of a verb refer to the properties of a verb. It can refer to the indicative, the subjunctive, the jussive or the imperative. Again, from my grammar book:

"The indicative mood is characteristic of straightforward, factual statements or questions, while the subjunctive mood reflects an attitude toward the action such as doubt, desire, intent, wishing or necessity, and the jussive mood, when used for the imperative indicated an attitude of command, request, or need-for-action on the part of the speaker."

I am too lazy to copy the examples in Arabic, but here's a few examples in English:
- Indicative: He leaves Cairo today.
- Subjunctive: It is necessary that we undertake a visit.
- Jussive (most often used to negate the past tense): We did not come.
- Imperative: Permit me.

I hope all of this helps, sorry if it's dense, I've tried to make it as simple as possible! My grammar book is this one, but it's very expensive and extremely detailed, which was very helpful throughout my degree, but you may want to look at cheaper grammar books like this one. A couple of other useful books about verbs include this book (cheap, easy to understand, not too long!) and this one (great for exercises).

Haha, it's ok, just mention the language next time, it'll make it easier to spot
And yeah, it's a lot of info to take in, it'll get better the more you practice, though !