\+61 (?:[01]\d{3}-\d{3}-\d{3}|0\d-\d{4}-\d{4})
In human language:
\+61 will match the country code +61 (need to escape the + otherwise regex interprets it as a quantifier)
The space will match a space, ie there *must* be a space after the country code.
You could put a quantifier after the space to make it optional: a + will match either 0 or 1 spaces, or a * will match 0 or 1 or multiple spaces.
(?: xxx | yyy | zzz) construct will match xxx or yyy or zzz etc
[01]\d{3} will match a 0 or 1 followed by 3 digits ie a 4 digit number starting with 0 or 1
[01]\d{3}-\d{3}-\d{3} will match:
a 4 digit number starting with 0 or 1, followed by
a hyphen, followed by
a 3 digit number, followed by
another hyphen, followed by
another 3 digit number
likewise,
0\d-\d{4}-\d{4} will match:
a 2 digit number starting with 0, followed by
a hyphen, followed by
a 4 digit number, followed by
another hyphen, followed by
another 4 digit number