Wow, I'm glad you asked. I'll cater this list specifically to direct effects of the ocean, but realize that the ocean absorbs CO2 directly from the atmosphere. So, I will provide some extra actions that also also capture the output of most greenhouse gas emissions. This list is ordered by the most impactful changes you can make to benefit the environment, and this case, specifically the ocean.
1) Change your diet. Stop eating fish and meat. Besides the "serial species depletion" currently taken place by our demand on fish, there is a lot of bicatch associated with certain types of fish. A lot of fishing practices are simply unsustainable. Ones that are would be certified by the (Marine Stewardship Council)[http://www.msc.org]. Also, if eating farmed fish is not a sustainable alternative. They alter entire ecosystems, demand many resources to stay productive, and create lots of waste. Also, most meat production has environmental impacts associated directly with oceans, such as groundwater contamination due to runoff from improper waste management practices at farms.
2) Live locally. Change your mode of transportation and travel habits. Stop driving a car, stop boating, stop flying in a plane, stop taking a train. Besides the dumping of sewage from cruise ships, by supporting any transportation method using fossil fuels, you're not only supporting the risk of oil spills. You're also contributing directly to CO2 emissions that are causing ocean acidification which has effects on some marine species. Also, a huge source of ocean pollution is litter and storm water runoff from our streets produced by copper on car tires that come off from your brakes.
3) Stop shopping for anything unnecessary. Anytime you buy something, it likely has some a relationship with an overseas country, which would mean it was shipped from somewhere far away. Good ways to assess the environmental impact of products are whether or not it is heavily packaged or over processed, and whether or not it was made locally. Try to buy products that are made in your area and that don't have packaging. All you really need to buy is food and toiletries.
4) Practice proper waste management. Refuse (disposables), reduce, reuse, recycle, and compost. Buy a stainless steel reusable water bottle/mug and bring it with you everywhere so you never have to use disposables. You can even bring your own reusable containers for leftovers at a restaurant or to bring your lunch to work. Use reusable produce nets and bags at the farmers market when you're shopping locally for that locally grown, fresh produce.
5) I actually think this is most important, but educate yourself on the issues. Things like ocean acidification, species extinction, and pollution are the three big issues.
Also, try to start volunteering doing beach cleanups, try to donate, get involved politically, and start educating others about the problem.