Numbers up to 20:

Cardinal Ordinal
0 noll nollte
1 ett or en första
2 två andra
3 tre tredje
4 fyra fjärde
5 fem femte
6 sex sjätte
7 sju sjunde
8 åtta åttonde
9 nio nionde
10 tio tionde
11 elva elfte
12 tolv tolfte
13 tretton trettonde
14 fjorton fjortonde
15 femton femtonde
16 sexton sextonde
17 sjutton sjuttonde
18 arton artonde
19 nitton nittonde
20 tjugo tjugonde

Note: Ett is neuter, en is uter; "the digit 1" is "siffran ett" in Swedish. Especially when counting, four is often pronounced as fyr. Nio and tio are commonly pronounced as nie, tie, respectively. Tjugo is usually spelled tjugi, and so on with the following multiples of ten (tretti instead of trettio, förti instead of fyrtio , etc.). Forty is never pronounced the way it is spelled (fyrtio), it becomes förti(o).

Multiples of 10:

Svenska English
tjugo (tjugonde) twenty
trettio (trettionde) thirty
fyrtio (and so on) forty
femtio fifty
sextio sixty
sjuttio seventy
åttio eighty
nittio ninety
(ett)hundra (hundrade) one hundred
(ett)tusen (tusende) one thousand
en miljon (miljonte) one million
en miljard (miljarte) one billion
en biljon (biljonte) one trillion
en triljon (triljonte) one quintillion

Other numbers:

Svenska English
10 000 tio tusen ten thousand
100 000 hundra tusen a hundred thousand
10 000 000 tio miljoner ten million

Particularity in writting the date:

1 842 artonhundrafyrtiotvå
2 013 tjugohundratretton (tvåtusentretton)

Note: To make numbers between these, you add a number 1-9 not in parenthesis, e.g. 55 is femtiofem, 73rd is sjuttiotredje, 20,000 is tjugotusen. However, tjugo is in this case commonly pronounced as tju, e.g. tjuåtta for 28. The -tio ending is commonly pronounced as -ti but not in the parenthesis case. Fyrtio is pronounced as förti and sometimes written as förtio. One commonly only say etthundra to distinguish it from e.g. tvåhundra. As you might have guessed, Swedish uses the same system for large numbers as e.g. the UK, not the system used in the US.