I assume you're getting a noticeable depth of water in a puddle against the house. We've had similar problems at our house, and they're pretty common around our area. You really should deal with this because it can cause all kinds of problems, like damaging your foundation. I also assume you have wood studs and supports somewhere behind the stucco, and if that gets soaked by standing water, it can rot or warp or do other damage.
Short term, you can get an electrically-powered utility pump and pump the water away. I've done that using an inexpensive 1/4 hp manual sump pump and a garden hose. You can find them at home centers or on Amazon, and they'll suck a puddle down to a small fraction of an inch. The downside is you have to be around when it rains to start and stop the pump manually. (For what you're doing, don't want an automatic pump with a float; they're designed to work in holes that fill with water, called "sumps".)
Long term, a lot depends on what things are like around your house. We live on a slope with a lot of "hydrostatic pressure", so our long-term solution was putting in a French drain uphill from the house to route the water away. Friends of ours used to live in a lowland area, and their rain problems happened because the water table would rise and flood their lawn; the solution was to dig a French drain, drop in a huge sump pump, and pump the water away. Since you're not super-experienced, I'd call a pro.