Two words. Simple right?
Like so many things, being supportive is often a conscious effort, day in and day out. It isn't about wanting the same thing and wanting to go about it side by side. This is about them wanting to do something, and you enabling them to do it.
Just walking down the street we hear people say things like, "I am here for you," or, "I am behind you." Sadly, when it starts to get difficult, these are often the people who bail and then try to convince the other person to bail.
"I totally support you in your new job! Wait, you're not doing so well? Well, let's get burgers instead."
What kind of support is that? I'm sorry, your fork is bent, you should definately give up on eating solid food forever.
When your S.O. decides to start something, especially something they are nervous about but really want, your responsibility grows along with theirs. Remember, you joined the relationship as a partner; not a judge, critic, or cheerleader. When she says, "I want to start selling armings. They're like leggings, but for your arms," don't reply with "whatever." Sit down with them and work to understand the product, the market, and most importantly, the reason why they are doing it. If she is going to take up painting, try to understand some of the basics like color theory, paint types, or even just look into art galleries.
Side note: before we go any further, we need to draw a line between being supportive, and being a "yes-man." A yes-man says okay to anything and let's her run with it. He does anything she asks and if she says she's done, then they bail. A yes-man never argues the idea even if he knows it won't work. He will never push her to become better at what she wants to do.
Being supportive is vastly different. You will need to think about the reasons she wants to do this action. Think about what it means to her and what she hopes to get out of it. Help her work out what she will do. Help her come up with ideas. Engage the project as if it were your own but do NOT take over or overrule their decisions. Find some way to help keep her on track or fi d the right track.
Doing all of this will prepare you for later when they hit a wall. Think about a time when you hit a wall at a job. Remember how difficult it was for you. Use that to help understand how they feel. This is really important because you may not be all that interested in the intricacies of what they are doing. It may not be a passion for you. It doesn't need to be. It is something they want.
Once you understand the problem, and the feelings about it, step to the side. Ask what she would like from you. Now for the hard part: do what she asks. If she just wants you to listen, then just listen. If she isn't sure how to proceed, tell her what you think.
Don't try to take over. Just simply be willing to engage in whatever manner she asks.
If you are still at a loss for how to support her, find an action she is planning for this thing. Maybe she is having a get together, an open house, a party, or a night out? Maybe she needs some time alone to work on her masterpiece, or just some time to unwind after an event she threw. Now, what can you do to take something of the preparation, or one of the road blocks, off of her plate? Maybe help clean up, or cook some food, be in charge of drinks, offer to take the kids for a bit. Find something to do that allows her more time to focus on the main part of what she wants to do.
In the end, being supportive boils down to finding lots of little ways to help her stay on target, while taking as much extra stuff out of her way as you can.