Big thing to remember about the new fishing rods is it's all modular, every time I mention empty slots to put things in below it means you can just swap out the items in them whenever you want.
First create a Fishing pole by using a Carving Knife on a shaft (1.0 kg) under Create > Tools.
This is a basic fishing tool that can only be used in shallow water for small fish. You may however notice that there is an empty slot inside for a "basic fishing line". You can make a basic fishing line by using your hand on a string of cloth (0.2 kg). Similar to the fishing pole there is an empty slot inside it for a (wood or metal) fishing hook and float slot. Note that you want the item called metal/wooden fishing hook not hooks (which is for tool belt creation). Floats are described here on the wiki: Floats. Inside the hook is where you can put Bait which can be covered from the wiki: Bait.
Now if you want to make a proper Fishing Rod out of the pole you have already got make sure to have no fishing line in it and then use the fishing pole on a shaft (if I remember this right the rod take on the shafts wood type). From there you need to add 3 eyelets (metal lump and small anvil). The rod is complete but again we have empty slots to fill inside it.
This time around the top slot is for a Fishing Reel. There are four types of fishing reels; Light fishing reel, Medium fishing reel, Deep water fishing reel, and Professional fishing reel. Placing one of these into the slot will change the name of the fishing rod to match. Inside the fishing reels is where you will now place your fishing line > float & fishing hook > bait. Each rod type catches different selections of fish though they do overlap on many, the big one to remember is that the professional rod is for the special fish. I'll cover the fishing lines first and then making the reels.
Each of these fishing reels uses a different type of fishing line which are created in a chain system where you make the basic one first, then use that to make the next in line and so forth. I'll just list them in order.
Basic fishing line (hand + string of cloth). Light fishing line (basic fishing line + spinning wheel). Medium fishing line (light fishing line + rope tool). Heavy fishing line (medium fishing line + spinning wheel). Braided fishing line (heavy fishing line + rope tool).
Now for the fishing reels themselves you need to be aware that there are fishing reels and then there are reels which are just building components for the fishing reels, I remember helping a number of people in the past that were confusing the two items. Each fishing reel takes a wood, metal or professional reel and is combined with a type of handle to make the fishing reel.
Light fishing reel (wood reel + handle). Medium fishing reel (wood reel + leather wound handle). Deep water fishing reel (metal reel + reinforced handle). Professional fishing reel (professional reel + padded handle). Note that the professional reel can only be made of steel or moonmetal.
Now similar to the fishing line before these other handles get created in a chain so I'll just list in order.
Handle (carving knife + shaft). Leather wound handle (handle + strip of leather). Reinforced handle (leather wound handle + wires). Padded handle (reinforced handle + square piece of cloth/wool).
Once you have your fishing rod kitted out you will likely want to take a look at the fishing chart on the fish wurm wiki page to determine what kind of bait you will want to use and what times you will want to be fishing to catch more of a particular type of fish as it has gotten fairly complex.