<1> There is a root विद्-ज्ञाने which means this dhAtu(root) has the meaning "knowledge". Then one forms a noun by adding a suffix called घञ्. In such a case the meaning of the word Veda would be (Repository of all) - Knowledge. विदन्त्येभिः धर्म-ब्रह्मणी क्रिया ज्ञानमयं ब्रह्म वा इति वेदः (Meaning: Through which Dharma and Brahman are known- the source of such knowledge = Veda.
<2> Here is another way of deriving the the word based on he dhAtu, विद्- सत्तायाम् [To be, to exist] . Explaining this in the style of Sanskrit learners - सत्तार्थक विद्-धातोः घञ्-प्रत्यान्निष्पन्नो वेद शब्दः(Meaning: The word Veda is derived by applying the suffix घञ् to the root विद् that is taken to mean "to exist". Now the explantion proceeds further as विद्यते सत्तां गृह्णाति व्स्तु अनेन इति वेदः(meaning: (Anything/Everything) exists ; Reality(Object) attains/comes into existence because of 'this'.
<3> There is a third route to arrive at this word. विद्-विचारे - Consider the dhAtu विद् with the meaning "to think/contemplate" ; विचारार्थकात् विद् धातोः 'अच्' प्रत्ययान्निष्पन्नः वेदः-- Applying the suffix 'अच्' to the dhAtu विद् which is taken to mean thinking/contemplating the word Veda is derived. Hence in the expanded form the meaning comes to be: विन्ते विचारयति धर्मब्रह्मणी क्रिया ज्ञानमयं ब्रह्म वेति वेदः- Dharma and Brahman are contemplated upon to be understood, for Brahman is Pure Knowledge or Pure Action.
<4> And there is a Fourth. विद्-लाभे -To obtain/gain.लाभार्थकत् विद् धातोः घञि वेदः - Starting from the dhatu विद् with the meaning to obtain or gain and applying the suffix घञ्one could derive the word Veda.The detailing of the same is: विदन्ते स्वरूपं लभन्ते वस्तु अनेनेति वेदः- Objects/Reality obtain their form by 'this' = Veda.
These four meaning for the root विद् are collected in the Siddhanta Kaumudi in the form of a couplet:
सत्तायां विद्यते ज्ञाने वेत्ति विन्ते विचारणे ।
विन्दते विन्दति प्राप्तौ श्यन्लुक्ष्नम्शेष्विदं क्रमात् ॥
If one begins(the derivation) from "Existence" then the verb(Third Person Sing) is विद्यते- It exists. If one begins from "knowledge"then it is वेत्ति - He knows. If one begins from "Think/Contemplate" then it is विन्ते- He thinks. If one starts the process of derivation from "Obtains/Gains/Attains it is either विन्दते or विन्दति. The last stanza of the couplet collects together the "modifying mid-fixes" due to these dhatus being in different gaNas.(Cf The question on Classification of Verbs).
Apart from the above etymological expalnation by lexicographers you have the following statements form the Veda Commentators. Sayanacharya says in the R^gbhAShyabhUmikA -विदन्ति-जानन्ति, विद्यन्ते-भवन्ति, विन्ते-विचारयति, विदन्ते-लभन्ते सर्वे मनुष्याः सत्त्वविद्यां यैर्येषु वा तथा विद्वांसश्च भवन्ति ते वेदाः। The same four meanings have been accepted for derivation by Sayana. He continues to say ... Humans learn the Science of Existence through which or where they would find this knowledge and then become learned such are The Vedas.
Source: Page 8, para 3,4: Vaidika-vA~NmayetihAsaH(In Sanskrit) by Acharya Jagadishchandra Mishra Pub: Chowkhambha SurabhAratI PrakAshan, Varanasi. (2009) Translated by MSS.