I would not consider that a small backyard. How big is it really there is no way from the pics to have real context. Post a to scale plan showing the space and how it realtes to the size of the house. To me you have a blank slate but budget will dictate what you can do. Are you handy and can handle lots of physical work ?If so this can be a porject maybe spread over a couple of years. Think about what you want from the space then start with an actual plan you work towards. Landscaping is something that can be done in sections over time. Myself I would do a patio quite large and all across the back of the house . Think of that space just like a house . An outdoor kitchen as simple as a BBQ some outdoor eating space , a seating area and if you want a hot tub Ilike them located with easy access to the primary bedroom. That will take care fof the outdoor use and with elbow grease from you not a huge expense . Then over time you start planting shrubs, trees etc . For now after the patio is done nice big pots filled with plants . Umbrelas to control the sun and you can do more than one . Post the plan here in jpeg format in a comment than all things related to this question dealt with here in comments DO NOT start another post.

Yes that’s a pretty small yard. How many people will live here? Kids? They’ll need room to run and play.

How big is the existing concrete pad? I think I’d start there with the pad, making sure it is an adequate size for several chairs at least, maybe a table and a grill. Say 12x14 to start. Down the road you could construct a pergola over it and then maybe extend the pad for a hot tub to set on.

Can you provide more information? Number and stage of life the occupants will be.

How you envision using the yard and how often you see yourself sitting out back or soaking in a hot tub or using a bbq. How much time do you want to spend maintaining the outdoor space?

Do you have dogs that will use the space? Do you mind seeing the fence?

Dimensions of the yard would be helpful.

Budget?

Do you already live here? Noticed you said this house, not my house.

What dollar amount are you thinking - small could mean $2k or $10k. Are you handy and do you enjoy DIY outdoor work?

I’m guessing by the Mesquite trees you’re in Texas?

What direction does the back face?

You haven't given us much information to work with--location, who will use the yard,--kids, dogs, guests, seniors, what planting zone you're in, budget, need for lawn.

Best approach is to go to a small garden center and ask them for names of affordable garden designers to create a long-term plan that you can implement in small stages. That way ou wind up with a yard with hardscaping, landscaping that works in your zone with a minimum amount of work. Patricia Colwell offered some great advice along these lines--extended patio with potted plants. Meanwhile, here's some inspiration:

Seating area that looks out at a mix of small shrubs, mulches areas with stepping stone pathway.

Rain Garden for Pollinators · More Info

Pergola over an expanded patio. Big box stores offer pergola kits in all sizes. Again, though, you need to decide about your patio size first.

Outdoor Pavilion, Pergola, and Patio · More Info

Thank you for you alls input!
This is the house we started our family, and now that we moved out we are considering making a short term vacation home. It is in Texas, so yes we get Lots of heat! I thought something to extend the concrete square in the backyard ( rocks ,bricks?)and something for a shade even one of those Home Depot yard/tent/shades ( don’t know the name). I will need to get somebody to do it.

Here are some pictures from Google Earth