Sindarin (and it’s conceptual precursors) have two major classes of verbs: basic verbs (based on an unadorned primitive verbal root) and derived verbs (produced with some kind of verbal suffix). In the literature, these two classes are sometimes called i-stem verbs and a-stem verbs after their present tense forms, which frequently have i or a respectively. For example, this terminology appears in David Salo’s book, Gateway to Sindarin (GS/111), though I am not certain he first coined these terms. I personally prefer the terms basic and derived as more consistent with Quenya terminology for these verb classes.
In Tolkien’s word lists, basic verbs are usually represented by stems ending in a consonant as in: ped- “to say, speak”. Derived verbs generally appear with stems ending in a as in: teitha- “to write”. These two classes date all the way back to the Gnomish Lexicon of the 1920s: G. cwed- “to say, tell” (GL/28), G. tectha- “to write” (GL/69). They appear in earliest known verbal inflectional paradigms, in the Early Noldorin Grammar of the 1920s, where Tolkien used ᴱN. mad- “to eat” and ᴱN. glathra- “to polish” as his main examples (PE13/126-127, 129). These early writings had other verb classes as well, mostly notably those resulting from vowel gradations in verbs with ancient syllabic ṛ, ḷ, ṇ; see Conceptual Development below for further discussion.
The Sindarin class of derived verbs ending in -a is expanded from what is seen in ancient Common Eldarin or in Quenya, where derived verbs are mostly limited to a small number of suffixes like -a, -ta, -ya, -na. Sindarin has additional wide spread suffixes like -ra, -la. Like Quenya, there are indications that some Sindarin derived verbs have strong past forms produced from the verb root rather than the verb stem, notable ôn the past tense of anna- “to give” (PE17/93); see the discussion of the Sindarin past tense for more details.
The details on how the individual verb classes are inflected is discussed in the entries on the more specific Sindarin verb tenses.
Half-strong verbs: We know that the Quenya class of derived verbs could be further subdivided into various specialized subgroups due to differences in ancient verb formation. There is compelling evidence that Sindarin (and Noldorin) had the equivalent of the Quenya class of half-strong verbs, which seem to be the origin of the Sindarin past tense for derived verbs. The best example is the causative N. tangad(a)- “make firm, confirm” < ᴹ✶tankāta-, whose conjugation is seen in the (currently unpublished) Noldorin Grammar from the 1930s, with (3rd-sg) present tangod and past tangant (PE17/44). This is consistent with what we know of its Quenya equivalent, Q. tancata- with half-strong past tancante (PE17/76).
There is at least one example of such a half-strong causative verb in Sindarin as well, covad(a)- “to make meet”, with present covad and past covant, a causative derived from cova (*koba) “meet” + ta (PE17/16, 158). But the best evidence for this verb class in Sindarin is the continued used of the past tense suffix -ant in derived verbs, which was probably generalized from half-strong past tenses. Tolkien alluded to this generalization in a brief note on the origin of the suffix:
Sindarin verbal history is complicated, and the use of -ant as a 3rd person past tense ending is rather like that of Medieval Welsh -as, or modern Welsh -odd. √TEK “make a written mark”: tekta- a derivative (from *tektā, Q tehta “a written mark”) gives the Sindarin verb stem teith-, of which the 3 sg. pa.t. is teithant (PE17/43).
As Christopher Gilson explained it in his editorial notes on this passage:
Tolkien’s allusion to the history of Welsh -as and -odd indicates that some similar analogical interchange underlies the relation between Sindarin past-tense forms echant “made” and teithant “drew”. As we saw above the -nt in the former results from strengthening of the root syllable with an n-infix, so that *et-kat- yields pa.t. *et-kantē > S echant. This could be the source by analogy of the -nt added to the stem teitha- (< tektā) to yield pa.t. teithant (PE17/44).
Gilson went on to describe the aforementioned conjugation of tangad(a)- from the 1930s Noldorin Grammar, where past suffix intruded into other verb classes, including (in the 1930s) basic verbs like mad-:
Colloquially owing to its resemblance to the “regular” -ant past tense (originally derived from -atā verbs [like tangada-]) it was reformed thus (in transitive verbs): medennin etc., 3 sg. madant [vs. original past tense mant] (PE17/44).
This generalization of common past tense suffix -ant from half-strong pasts remains the best explanation of this Sindarin suffix, which is in turn implies the continued existence of a class of half-strong Sindarin causative verbs.
U-verbs: We know that Quenya (and Common Eldarin) has a class of u-verbs whose verb stems ended in u. It seems quite possible such verbs existed in Sindarin as well, but there are no attested examples and we have no real idea how they might be conjugated. It seems probable that there are further complexities to the verb class system of Sindarin which we simply cannot analyze at this time due to lack of evidence.
Conceptual Development: As noted above, Gnomish and Early Noldorin had some verb classes that were the result of verbs with ancient syllabic ṛ, ḷ, ṇ for their vowel, which resulted in vowel gradations due to the differing developments of short and long syllable consonants. For example: G. grith- “care (for)”, past †gardhi from the root ᴱ√GṚÞṚ (GL/42), where gṛþ- > griþ- but gṝþ- > garð-. Similarly, ᴱN. gurdh- “to die”, past gwardhaf from the root ᴱ√GWṚÐṚ (PE13/132; QL/104), where gʷṛð- > gurdh- but gʷṝð- > gwarð-.
See the entries on the various verb tenses for further discussion.