"besoin" is not a verb but a noun!
"to need" in French is actually a combination of a verb (avoir) and a noun (besoin).
"Avoir besoin"

J'ai besoin de toi.
(I need you)

J'avais besoin de te parler.
(I "needed" to talk to you)

J'aurais besoin d'aide.
(I [would] need help)

etc.

This is a very good example of how literal translation can't always work.

In French, you don't "need", but instead you "have need (of)". Other languages deal with the concept of "need" in different ways, so we need to be open to the differences.

I should also add that verbs in French are separated into three groups:

First group: 
-er
(aller, manger, danser)

Second group:
-ir
(Finir, grandir, grossir)

--> Trick to spot them: when you conjugate them at the first person of plural in present tense, you find the end "issons"
Nous finissons, nous grandissons, nous grossissons. 

Third group (irregular verbs)

-ir
(accueillir, appartenir)

--> Nous accueillons (and not "nous accueillissons", see?), nous appartenons

-oir
(apercevoir)
-re
(boire)

So, as you can see, all verb endings contain one "r" somewhere. That should help you spot them! Therefore, you could easily deduce that "besoin" is not a verb.

However, be aware that not all words that end with "-er, -ir, -oir or -re" are verbs. 

For instance "avenir" is the noun for "future"

Hi there! 

So I see you are looking for the conjugation of "besoin". So the slight difficulty with "besoin" is that is always is formed with the auxiliary "Avoir".  This is probably why you cannot find a direct conjugation for Besoin. 

Therefore, the conjugation that you need to learn here is actually for avoir, not for besoin. So, for example, the present tense of "besoin" is formed like this:

J'ai besoin

Tu as besoin

Il/elle a besoin 

Nous avons besoin

Vous avez besoin

Ils/elles ont besoin.

So, in each tense, you need to conjugate "Avoir", and besoin stays the same. You should also note that "Besoin" is always formed with "de". For example, "J'ai besoin de nourriture" = I need food.

I hope this helps you!