I am assuming the conviction was in WA? And have you had any convictions since then? What was the offence? And were you sentenced to prison? If so how long?
In WA you can apply to have your criminal convictions spent after a waiting period. A spent conviction will not appear on your standard police check, nad you can state that you have no convictions. However there are still jobs which will require you to disclose a spent conviction on application and certain other instances where you must declare a spent conviction. You can read about that here:
What spent conviction orders do
The waiting period is generally 10 years plus the length of any prison term imposed, however if you were a minor at the time of the conviction it is only 5 years plus prison term. So you can probably apply to have your conviction spent in a few years, depending on whether you served jail time.
In the specific case of convictions for possessing cannabis (but not possessing a cannabis plant, cannabis resin or any other cannabis derivative) or an offence of possessing a pipe or smoking implement containing detectable traces of cannabis, the waiting period is 3 years, as long as the conviction for that offence occurred on or after 1 August 2011.
How you apply to have the conviction spent will depend on whether the offence is classified as serious (more than 1 year jail or $15,000 fine)
Applying for old convictions to be spent
