Starting Point: What is your approximate location on earth?

It looks like most of your yard is mostly full shade during the growing season. That can be a challenge to work with. Do you have any children or pets? Sometimes some plants can be a concern for kids or pets. Do you plan on putting in any fencing along that green line, or prefer to let your plants be more of a living border for the yard?

If you aren't doing so already, plan in a composting space. Dropped leaves and green garden scraps help make great compost fto feed your gardening plans.

Alex, start with a plan. Many full-service nurseries offer a design service at a very reasonable cost. They sometimes offer discounts on plants, too. If you don't have success there look for a small, local company that does design, installation and maintenance. You have mature trees and an existing deck so a landscape designer can help you incorporate those elements into a plan that meets your budget.

Once you have a design you can decide what you want to DIY and what you want someone else to do. You can also complete the plan as time and money is available. Good luck with your project!

R, I'm in Maryland

@Beesneeds, the right side of the yard gets some sun during the day, so that's where I would put some kind of vegetable garden, perhaps. As for the fence, I think I prefer to let plants be a living border for the yard. Good idea on the compost, do you have any particular composting bin in mind, or anything will do?

@einportlandor I love that advice, I have started liking in my neighborhood for local landscaping business recommendations!

What to do for composting bin depends on your style of composting. Some folks like to be active and have a hot pile or few that they turn and add to regularly. Hot piles break down and finish faster. Hot piles can be better if you want more compost quicker, or have limited space for your composting and can't let cold piles sit for years. I can't recommend what bins or system works best for that, I don't hot compost. There are other members here that do hot compost and are great at it. If you post a couple pics of your yard and ask for help setting up compost bins for that over in another section, you will likely get some help with that.

I'm a lazy gardener and have the space in my yard that I can do cold composting. I do square cages of 2x4" metal fencing, cubes about 3x3x3'. Fill them up with the garden debris till they are full and let them compost down for a few years. I like to top them off with good garden dirt and grow short crops in them since they are super raised beds at that point. I also have a lot of open garden bed space, so most of my fallen leaves are used for mulching beds. As you landscape in your borders you may find you want to use your leaves as mulch instead of bringing in bark or something else.

If you post a topic similar to this one but addressing your composting, veggie gardening, and shade plant requirements you can get help from additional members that are more active in other areas here. Post in the Soil, compost, and mulch, the Vegetable Gardening, and the Gardening in Shade sections and include the photos of what you are wanting to do.

What are the trees you’d like to “ relocate “ ? I’m not seeing any small saplings.

I'd start with a small veggie garden in the sunny spots. You can buy or build a simple raised bed. This will give you a nicely defined garden area. You can also make a garden directly in the soil, but you will most likely need edging to keep lawn grass out.

Your state extension office is a great resource:

https://extension.umd.edu/resources#!/category/3

How sunny are the sunny spots? You'll need at least 6-8 hrs of sun for lettuce and other greens and 10 hours for tomatoes, peppers.

Observing. That's where to start. Spend an entire day outside in another month. What time does the sun start hitting those sunny spots, and for how long? What views do you get when you sit certain places? Can you capitalize on them, or avoid looking at eyesores? You may want to move your patio someplace completely different, for instance. What if, instead of the long portion heading towards the shed, you have it go longways towards your widening stairs? You might end up with more sunny spots to use. For instance. Since you've suggested rebuilding altogether. I feel like your deck is encroaching on what could be your best gardening spot ;) But that's just me. What do you feel when you're in the space, with a clean slate? If none of it was where it is now? This is all just an exercise in, is my yard at my maximum. Maybe you can't move your deck and it's in its best spot.

Unless the trees you plan to move are small, you are better off moving them after a year. In the spring, you dig a semi-circle the width of the tree's crown the depth of the roots. This cuts half the roots and the tree will grow new roots inside the circle. Then, in next spring, you do the other half of the roots (the semi-circle you didn't cut in the spring). Then, you move the tree the following fall.

@Iova Blooms, the link you provided is really great! It was wealth of information, and great ideas for pants in Maryland. Thank you! 

I think my yard's soil is pretty bad: dry and kind of sandy, so I'm hesitant to plant into it. Would it be helpful to add a layer of some kind of nice soil to the areas I'll be growing plants? I'm scared I'll plant them and they will die!

You improve soil by adding organic material.

Alex -- Your state Extension Service likely has loads of helpful advice on their website that's specific to your area. Do a bit of googling. While you're at it, track down your local Master Gardener chapter (managed by the Extension Service). Master Gardeners can talk to you about your soil and point you to great resources -- their service is free.