Why do our continents look the way they look today?

Overall, this is due to plate tectonics--the movement, creation, and destruction of lithospheric plates which float on the asthenosphere, with the associated volcanism, uplift, sinking, and mountain building.

Shaping Continents and Seas

The shape and location of the continents and islands are due to several related geologic processes, some of which occur extremely slowly:

• Continental drift (combines landmasses, creates mountains and other landforms)
• Volcanic activity (creates lava plains, islands, and volcanic peaks)
• Weathering and erosion* (reduces mountains and hills, creates rivers, lakes, deltas)
• Tides and currents (erode or create coastal landforms)
• Air temperature and circulation (rain and ice can create glaciers or icecaps, which trap water and reduce sea levels)

*The process of sedimentation can form new layers of sedimentary and metamorphic rocks, which can be uplifted or eroded as well.

*The biological organisms of Earth can affect erosion and also the climate, which can athereby cause changes to the land and seas.
I think our planet's continents look the way they do today because of the oceans volcanoes spreading apart over time.

That's a start. The volcanoes are the effects more than cause.

The continents are vast rafts of (essentially) granite floating on the Earth's viscous Mantle, through a thinner, fractured, surrounding sea-floor crust.

These "tectonic plates" break and drift, driven by movements - probably convection-currents - in the Mantle, which is the bulk of the planet's volume.

The ocean crust thins and breaks, forming a line of extrusive, relatively docile eruptions and basaltic lava floods along the "mid-ocean ridge", and forcing the two parts of the plate apart, against the surrounding continents. E.g, Mid-Atlantic Ridge, Iceland as the Atlantic Ocean is still widening at about 20-25mm/year mean speed.

(Continents too can thin, rift and separate, as presently occurring in NE Africa.)

The ocean crust approaching a slower-moving continent is forced below it - subduction. It melts in the Upper Mantle to produce magma that slowly floats up through the continental crust to form either huge solid masses called "batholiths" or "plutons" below ground, or be expelled as lava in explosive eruptions. E.g. those of the "Pacific Ring of Fire"as the Pacific Ocean is closing.

Subduction is also responsible for the most destructive earthquakes, from the stick-slip action on the thrust-plane between continental and subducted sea-floor plates.

Eventually the continents collide, to buckle, fault and fold the continental crust and its sedimentary cover into mountains. E.g., Andes, Alps, Himalaya. The sedimentary rocks caught up in the process over the millions of years this all takes, are compressed and heated to form "metamorphic rocks".

So to summarise, the continents owe their shapes to Continental Drift - a continuous, continuing, breaking and colliding as the tectonic plates are shuffled around the planet.
because they were once connected, called "Pangaea"
Pangea, or giant land mast, caused our continents to look the way they do. But how? The continents slowly drifted a part.. Look at a map, you can see some continents could fit together.