Just relax and you will do fine. At the basic level you will be tested at, plant and animal cells are not difficult. Plant and animals cells have a lot of things in common, so we should focus on those first.
Below are very basic drawings of the two types of cells.
I know it can seem overwhelming at first. So many parts to learn. However, a lot is just common sense and many of the parts between the two do the same thing. The easiest part is the outside. In a plant it is called the "Cell Wall" and is just like your house has a wall to keep things out. Think wood house and plant. Easy, right?
An animal cell has an outside too, but it is not a house wall, but called a Membrane. Just like meat in a supermarket has an outside membrane you often need to remove before cooking it. They both protect the inside of a cell, but the animal membrane is not as strong and does a lot more things.
All the empty space inside both animal and plant cells contains liquid to keep the parts from getting damaged and lets them float around to move, like in a swimming pool. The liquid is called Cytoplasm. Think blood "plasma".
Both types of cells have a Nucleus. The Nucleus means "kernel" and it is located in the center of the cell. It is where all the DNA is stored and the most important part of the cell. It is like your brain and tells the cell what to do. Inside the Nucleus is a smaller section called the Nucleolus. Just think little Nucleus. That is not as powerful and does not hold DNA, but it does other important stuff like make things for the cell, such as proteins and RNA. Inside the Nucleus is a Nuclear Membrane that does what it sounds like and just holds it together.
Doing good so far I hope 
Both cells have parts to make energy, just like we have a stomach and the ability to get energy from food. That part is called the Mitochondria. Think "Mighty Power". It takes in food particles from your blood, or in a plant from the roots, and digests them into energy pieces the cell can use called ATP. It fuels the plant, just like gas in a car.
Cells need to make stuff, like proteins. It is one of the most important things they do for us. A part in both plant and animal cells called the Endoplasmic Reticulum (ER for short) does this. It is like a factory and makes things. Think "Plasmic/Plastic Factory." There is Rough part that is literally rough when you see it called the Rough ER and another section that is smooth called the Smooth ER. The Rough part makes things and and the Smooth section is more like the shipping department in a factory and is used to move things out to the cell. Think Smooth Move. The Rough ER uses something called Ribosomes to help them make things. Think "Robot Somes" and they are like the workers in a factory. They make the Endoplasmic Reticulum "rough" and also can be found floating around the cell in the plasma.
Okay, we are almost done, just a little more to go and you will have mastered cells
We now come to the Golgi Body. Cells need a way to package things up and move them out. They work with the Rough and Smooth ER (factory that makes things and prepares them for shipping) and are like the FedEx trucks for the cell. It puts stuff in packages so they can be moved and used. Think moving Golf Carts (sounds a little like Golgi) that move around a course.
You will also see a Centrosome in both cells. A Centrosome is used when the cell needs to divide. When a cell is ready to divide these parts come into action and move to the Center of the cell and attach tiny threads between them that later start things going in a complex process called Mitosis. Just think Center and cell body division. "Soma" means body. So Center Body.
We now come to differences.
A plant cell has a Vacuole which takes up most of the space and gives it support. It is mostly just empty with fluid, so think empty vacuum. It keeps a plant from falling over. Animal cells don't have it.
The next difference that you probably already know are that plant cells have Chloroplasts that make Chlorophyll. A plant uses water and sun energy to make food it needs to live called chlorophyll. It would be great if animals could do this too, but we don't and need to eat food instead.
Only Animal cells and not plant cells have a Lysosome. They are like garbage trucks that can take molecules and break them down into waste. They then move to outside of the cell and dump it into the blood stream. Think "Lysol" disinfectant spray that kills germs.
If you got this far and are still reading, Congratulations
We have covered all the main parts of both cells. Best of luck with your studies! Let me know if you have any questions.
