Domain Authority is difficult to influence directly. It's measured using an aggregate of metrics.
DA is based on three main factors:
- Domain Age
- Domain Size - Number of pages of content
- Domain Popularity - Number of quality Incoming Links
The best way to increase your DA is to improve your overall SEO. So make sure to check your onsite optimisation first. Get the technical SEO up to decent levels.
Then focus on your link profile. Get backlinks from relevant, quality sites. The best way to do that is write high quality content that people would want to share and link to.
Whatever you do, don't try to automate the link building process.