The following is based mostly on Clackson and Horrocks 2007/2011, Leumann 1977, and Wallace 2011.
First of all, something to keep in mind, as Weiss 2009/2011 puts it, is that
"Long vowels were generally not distinguished in Latin orthography" (p. 29; emphasis mine - Alex B.). That being said, there were four exceptions.
- Geminatio vocalium (the double writing of a long vowel):
used primarily between 135-75 BCE, "sporadically also later" (Clackson and Horrocks); inspired by Oscan; this tradition goes back to "[usque ad] Accium et ultra" (Quint.), cf. Velius Longus "nam nec Accium secuti sumus semper vocales geminantem, ubicumque producitur syllaba" ("For neither do we follow Accius in always geminating vowels whenever the syllable is long" - transl. by Weiss).
was used only sometimes; mostly limited to the first syllable of a
word; mostly restricted to A (less so with E and V; virtually nonexistent
with I and O):
Some examples from Leumann:
AA: aara, maanium, faato naatam, paastores, Vaalus, Vaarius; famaa;
EE: ree, seedes, Sullai Feelici, leege;
VV: Luucius Puupius, cuurauerunt, iuure, arbitratuu
OO: uootum, Vrsioonis
- I longa:
occasionally, in use from around 110 BCE; no longer in use in the imperial period. Weiss calls it "a kind of i on steroids."
Examples: FELICI, VICVS
cf. "nec quicquam meliust mihi, ut opinor, quam ex me ut unam faciam litteram longam laqueo collum quando opstrinxero" (Plautus, Aul. 77); "The best thing for me, I suppose, is to tie a good tight noose around my neck and to stretch myself into one long letter" (transl. by W. de Melo)
NB: I longa was also used for other purposes (e.g. decorative short i or the close articulation of short i before another vowel).
long u: oi, oe, ou (from 100 BCE until the imperial period)
long i: ei (between 150-70 BCE) Sullae Feleici (cf. Felicei)
- the apex:
in use from the end of the OL period (MV́RVM, 104 BCE); various shapes, coronis and acutus; ousted the first three; Leumann writes that its use was non-binding and rare, cf. "aber auch dessen Anwendung ist nur ganz unverbindlich und selten"
Quint. "longis syllabis omnibus adponere apicem ineptissimum est"
The apex was inscribed over i in exceptional cases only (that's why some researchers choose to say never).
To give you an idea how frequent the apex was, let's take a look at a fragment of the Laudatio Turiae (late 1st century BCE). There are eleven lines in this fragment and only two occurrences of the apex (órnamentis in line 2; domús in line 9).
I wrote about macrons already.