There are 23 elementary cardinal numerals (bazaj numeraloj):
nul – 0
unu^[16] – 1
du – 2
tri – 3
kvar – 4
kvin – 5
ses – 6
sep – 7
ok – 8
naŭ – 9
dek – 10
cent – 100
ok – 8
naŭ – 9
dek – 10
cent – 100
mil – 1000
Other cardinal numerals are formed by combining these elementary ones:
dek unu – 11
dek tri – 13
dudek – 20
dudek kvin – 25

tridek – 30
okdek – 80

cent kvin – 105
cent tridek ok – 138
naŭcent – 900

mil ducent kvardek sep – 1 247
tri mil – 3 000
dudek mil – 20 000
cent okdek unu mil kvarcent naŭdek tri – 181 493

Numerals 1 to 999 999 can be expressed by the following formula N:
N = [ [ I’ ] * mil] + [ I ]
I = [ [ du-naŭ ] * cent ] + [ [ du-naŭ ] * dek ] + [ unu-naŭ ]
I’ = [ [ du-naŭ ] * cent ] + [ [ du-naŭ ] * dek ] + [ du-naŭ ]

The interpretation of the resulting numeral is the following: Elementary numerals are replaced by corresponding numbers and + and * are treated as classical arithmetic operators.

The cardinal numerals can be viewed as nondeclinable adjectives. Counted things are normally declined (and in plural, if the numeral is other than unu).^[17]
unu viro – one man, kvin viroj – five men
Kvin amikoj iras en arbaron. – Five friends go to the forest.
La instruisto laŭdas kvin lernantojn. – The teacher praises five pupils.

The numeral unu can be used as a pronoun. In that case, it is declined.
Unuj legis, kaj aliaj skribis. – Ones have been reading and the others have been writing.
Estas facile unujn ami kaj aliajn malami.^H – It is easy to love ones and to hate others.
There are different opinions about the accusative form of the pronoun unu in singular. Some authorities^[18] say that it is not correct to add the accusative ending n with unu in pronominal function. The reason is that it is hard to distinguish between numeral and pronominal unu (in contrary to the form unuj, which can be only a pronoun). Some authorities^[19] are not so strict and just say that the absence of n is illogical, and has no other than historical reasons.

Numerals as miliono – 10⁶, miliardo – 10⁹, biliono = duiliono – 10¹², etc. are nouns^[20] and are normally declined:
Mi havas unu milionon. – I have one million.
Mi havas dek milionojn. – I have ten millions.
and counted objects are in prepositive using preposition da:
Cent milionoj da dolaroj. – Hundred millions of dollars.
There is no strict rule about mixed expression (noun numerals with pure numerals)^[21]:
Li havas dek milionojn tricent mil naŭcent sepdek ok da dolaroj. = Li havas dek milionojn tricent mil naŭcent sepdek ok dolarojn. – He has $10 300 978.

Other than cardinal numerals are formed by suffixes and endings added to the last part of the cardinal numeral. The spaces between parts of the cardinal numeral are replaced by hyphen.
trimil okcent dudek kvin – 3 825
trimil-okcent-dudek-kvina – 3 825^th

Ordinal numerals (Ordaj numeraloj) are formed by adding the adjective ending a:
unua – first
dua – second
mil-kvincent-sesdek-tria – 1563^rd
You can also form an ordinal numerals from a numeral noun by replacing the noun ending by the adjective ending: miliono ◊ miliona
Nia miliona kliento ricevos specialan donacon.^M – Our millionth client will receive a special present.
Ordinal numerals are normally declined as adjectives:
Mi skribas trian ĉapitron. – I am writing the third chapter.

Adverbial numerals (Numeralaj adverboj) are formed by adding the adverbial ending e:
unue – for first time, first (in a list)
due – for second time, second (in a list)
mil-kvincent-sesdek-trie – for 1563^rd

Names of numbers are formed by adding the noun ending o:
unuo – number one
duo – number two
cento – number hundred
kvincent-tridek-sepo – number five hundred thirty seven

Multiplication numerals (multiplikaj numeraloj) are formed by the suffix obl.
triobla – three as much in size, strength, number, or amount
trioble – three times
trioblo – a number or quantity three times as great as another
triobligi – to make something three times bigger, larger, etc.
or by suffix foj:
trifoja – occurring three times
trifoje – three times
trifojo – an occurrence three times
trifojigi – to make something occurring three times
There is a difference between obl and foj: The former means multiplication, the latter repetition.
duobla pago – salary two times as big as normal
dufoja pago – salary paid two times to the same person

Collectives (kolektivigaj numeraloj) are formed by the suffix op:
duopa – having groups of two
duope – in groups of two
duopo – group of two, a pair
kvaropo – quartet
marŝi kvarope – march in groups of four

Fractions (frakcioj) are formed by the suffix on:
duono – half
duona – being a half
duone – to the extend of one half
duonigi – to halve
Counted objects after fractions are connected with the preposition de (not da).
Duono de ni mortos.^A – One half of us died.
triona horo = triono de horo – three quarters of an hour
Li faris sian taskon nur trione.^A – He did only one third of his task.
La tanko estas duone malplena. – The tank is half-empty.
Nominal fractions are normally declined:
Li donis al mi duonon de sia pano.^M – He gave me half of his bread.
Li trinkis duonan litron da lakto.^M = Li trinkis duonon de litro da lakto.^M – He drunk one half of the liter of the milk.

Distribution^[23] (distribuo) of objects is expressed by the preposition po:
La gastoj trinkis vinon po du glasoj.^A – Each guest drunk two glasses of wine.
La gastoj venis po tri. – Guests came in groups of three.
Ili ricevis po kvin pomojn. – They received five apples each.
Prenu la medikamenton po 20 gutoj. – Each time you use the medicine, take 20 drops.
From po, you can form also an adjective – poa, and adverb – poe:
Ili ricevis poan korbon da pomoj.^A – They received a basket of apples each.
Tiuj studentinoj havis poe plurajn amantojn.^A – These girl-students had more lovers each.
These forms are rare, because poa = po unu, and poe = po.

I have not covered many topics that are not important for morphology – how to express dates and times, problems of using numerals with some prepositions, mathematical expressions, etc. These topics are thoroughly covered in PAG §87G & I or PMEG – http://purl.oclc.org/NET/pmeg/pmeg10/nvq.htm

^[16] In special occasions (counting things) it is possible to use un’ instead of unu. (PMEG – http://purl.oclc.org/NET/pmeg/pmeg10/asqnor.htm):

Un'! du! un'! du! - La soldatoj marŝis.^M – One, two, one, two – soldiers marched.
"Un', du, tri, kvar", li kalkulis laŭte.^M – “One, two, three, four”, he counted loudly.
However, it is impossible to use that form in normal sentences: *Mi havas nur un' amikon.^M – I have only one friend.
^[17] There is no rule about number of the counted thing after nul. PMEG (http://purl.oclc.org/NET/pmeg/pmeg10/jfquzasp.htm) says that it is preferred to say neniu, if it is possible: Post tio restos nul homo(j). = Post tio restos neniu(j) homo(j). – After that nobody will stay., Mi aĉetis nul komo kvin kilogramo(j)n da rizo. = I have bought 0.5 kilograms of rice.

^[18] See (PMEG) – http://purl.oclc.org/NET/pmeg/pmeg10/nvqbazun.htm
^[19] See Kalocsay, Waringhien: Plena Analiza Gramatiko de Esperanto (PAG), 1985, §64

^[20] In the past, for 0 only the noun nulo was used. Today the form nul is normally used, and the form nulo is used for the name of the number – similarly to many other numerals kvin – kvino, dek – deko.

^[21] See also PMEG – http://purl.oclc.org/NET/pmeg/pmeg10/nvqmik.htm
^[22] See also PAG §87A-F, PMEG http://purl.oclc.org/NET/pmeg/pmeg10/nvq.htm – Nomboroj
^[23] See also PMEG http://purl.oclc.org/NET/pmeg/pmeg10/rv_po.htm, PAG §87C