Insecticidal soap in a spray bottle will get the aphids without poisoning your garden and yes you do need to take action. Since you are a new gardener I'm going to give you some environmentally safe pest control solutions that you can print.

Insecticidal soap will kill most soft bodied insects. I usually add about 1/2 teaspoon of any mouthwash that contains alcohol to my spray bottle for extra oomph

Neem oil kills a lot of pests like flea beetle

For slugs use Safers slug bait.Sprinkle it on wet ground in the evening

To be sure that's what you are dealing with take a flashlight out after dark and check because it could also be earwigs if you see damage and don't see anything on your plants in the day. Both slugs and earwigs hide in the day and feed at night. This is what I use for earwigs. I've taken it from my pest file

Bait for Earwigs.

Equal
parts of full salt soy sauce, cooking oil and (molasses or corn syrup). The molasses or
syrup is bait to attract them--the oil doesn't allow them to crawl back out and
the salt in the soy sauce finishes them off and makes the mixture dark so they
think it is just a hole. Put it in a small container— I use those small scoops
from laundry soap and place a stone on top but you can use any small container
even the bottom of a soda or water bottle
and anything for a lid. Cover 1/2 inch of the bottom of the
container with the mixture and bury it up to the brim in the soil where you
have a problem with them. Prop a lid over it so it doesn't get diluted by rain
and so it is a nice dark place for them to hide for the day--ha. When you prop
the lid, leave a small space for them to crawl into the container. You might
have to wait a couple of days for it to work, but the first time I tried it I
used a baby food bottle and it was full to the brim with little grey baby
earwigs the next morning. I was surprised at just how many I did get. Try it.
It really works.

Cut worm will cut off a plant just above the ground and feed on the roots. The cutworm moth will only lay 1 egg in the same spot so if you see a cut off plant dig down under it and you'll see a fat grub. Dig it out and step on it.

These are the most common garden pests but there are others. With all these you may have repeat the spraying--etc. One application may not be enough. Try and get pests at the first signs that you have a problem so they don't have a chance to multiply.

You will learn as you go along but I hope this will help a bit.

Good luck and enjoy your gardening

I forgot to add that the best time to spray is in early morning or around 5 or 6 at night or when they are in the shade. Wet plants will burn in the sun and wet plants at night will invite fungal diseases. You want to allow time for plants to dry before the hot sun hits them or the cool night air keeps them damp