Almost certainly neither quickly nor easily. When a judge issues a failure to appear warrant, it is because the person has already demonstrated they would not show up when required. That history makes the judge very unlikely to offer bail again or release someone on their own recognizance, because the entire purpose of bail is to secure future appearances, and that trust has already been broken.
In most failure-to-appear situations, the judge remands the person to custody without bail. That means they stay in jail until they are brought before the court. At that point, the judge decides how to handle the missed appearance, whether to impose additional penalties, set a new court date, or address whatever the underlying case was.
In some cases, particularly for minor underlying charges or first-time FTA situations, a judge may set a new bail amount, but it is often higher than the original to reflect the increased flight risk assessment. Expecting an automatic release the same way one might after a standard arrest is not realistic.
The most important step at this point is getting to an attorney who can appear before the judge and argue for the most favorable terms possible on the FTA, whether that means arguing for release with conditions or addressing the underlying case as quickly as possible.