Leader Leanne Wood said her party accepted the referendum result to leave the European Union, but claimed no part of the UK voted for a "hard" Brexit.
In an article for The Times, she said the Welsh Government should not "sit back and let Brexit take its course".
Meanwhile First Minister Carwyn Jones has told AMs that UK ministers will have to compromise on immigration.
Ms Wood said the UK was "still in the dark" four months after the June vote on what the result meant.
She said Plaid accepted the High Court ruling that Parliament must give its approval for the triggering of Article 50, to formally launch the two-year process of the UK's departure from the EU.
Ms Wood said the ruling "should not be seen as an opportunity to overturn the result", but gave an opportunity for the 48% of voters who backed Remain "to have an input" and pursue a "soft" Brexit.
She accused the UK government of making "nothing but contradictory statements, with comments from one minister ridiculed by another", and claimed the Welsh Government had been "at best incoherent and at worst utterly clueless" in its response to Brexit.
"Wales voted Leave, but it does not mean that the Welsh government should sit back and let Brexit take its course," Ms Wood wrote.
"Our exit from the EU will be one of the most pivotal moments in our history and it is vital that both governments get it right."
Stressing her party's preference for continued membership of the single market, Ms Wood said Plaid AMs and MPs would table written questions on Brexit every day until ministers in both Westminster and Cardiff Bay gave a "satisfactory outline" of their intentions.
"People need and deserve answers, and Parliament needs answers before it can be expected to support the triggering of Article 50," she said.
People need clarity on what Brexit means for both the UK and Welsh governments, Plaid Cymru has said.