Here are some tips for taking on art commissions as a budding artist:
Build up your portfolio. The more work you have to show clients, the more likely they are to commission you. Photograph or scan pieces you've done and create an online portfolio on a site like ArtStation, Behance, or your own website.
Set a price list. Determine a price list for different types of commissions, e.g. portrait $50-100, full body $200-500, landscape $200-1000, etc. Factor in the time, materials, and skill required. It's best to start on the lower end until you gain more experience. You can always raise prices over time.
Promote your services. Spread the word about your commission services on social media platforms like Instagram and Facebook, local Facebook Marketplace groups, and among friends/family. Offer promotions and discounts to help get your first clients.
Find your niche. Identify a specialty that you want to focus on, e.g. pet portraits, fantasy landscapes, children's book illustration, etc. Build up your skill and portfolio in that niche. Specializing will make you more appealing to potential clients interested in that subject matter or style.
Set clear requirements and boundaries. When a client contacts you for a commission, be very clear about what you need to get started, e.g. photos, dimensions/medium, deadline, deposit. Set boundaries to avoid scope creep, such as limiting the number of revisions. Get everything in writing to prevent misunderstandings.
Deliver quality work on time. Fulfill the commission to the best of your ability, and remain in contact with the client during the process. Deliver the final piece on or before the agreed deadline. Satisfied clients can lead to repeat customers and word-of-mouth promotion.
Increase prices gradually. As you gain more experience, skill, and positive reviews, you can raise your prices over time. But do so incrementally, e.g. 10-30% per year. Never lower your prices, only offer discounts for promotions. Value yourself and your work!
With practice, you'll get better at finding and fulfilling art commissions. The keys are building skill, setting clear policies, delivering quality, and increasing your rates as your reputation grows. Good luck!