There are many different ways to make cordials, but they all combine a few basic ingrediants. Alcohol, sugar, fruit and seasonings. You can follow set recipes or you can just jump right in a try it out. If you just want to experiment, it is hit and miss, but it can be quite fun. Remember to write down everything you did so that you can recreate it next time. Some cordials take longer to mellow than others (berry cordials are usually finished pretty fast). A friend of mine made a peach cordial that she hated until it had sat for a year or two and then it was wonderful. So what you first thought was a failure may later turn out to be a success. If you are nervous about experimentation, there are many recipes online and several good books such as "Kitchen Cordials" by Nancy Crosby and "Cordials from your kitchen" by Pattie Vargas and Rich Gulling.
Vodka is mostly used because it has little flavor of its own, so all of the flavor you get comes from what you add into it. Some people swear that you must start with a good vodka, but I have used cheap vodka in the past and gotten good results. You can also run the cheap vodka through a Brita filter pitcher to get a higher quality of vodka. Other alcohols such as brandy or rum can be used, but they will add some flavor to the drink.
The sugar can be white sugar (cane or beet), sugar in the raw or honey. These will all impart a slightly different flavor. The white sugar is sharper while the honey is more mellow. Some people swear there is a diffenrence between beet sugar and cane sugar, but I have not noticed it. I have not tried sugar in the raw yet, but I imagine it will give a flavor in between the white sugar and the honey. Honeys have different flavors based on the flowers the bees fed on. Some of the dark honeys will give a different flavor than the lighter honeys like clover. If you don't want to interfere with the taste of the fruit you are putting in, stick with the lighter honey. I have not tried corn suryp, but I imagine it would work. I would not use it because it is so heavily processed that it is barley a food anymore. You can also omit the sugar at this point and add a simple suryp or honey later, but I always add the sugar right away.
The seasonings must be carefully chosen to complement the fruit being used and because they can easily overpower the flavor of the fruit. Many cordials have been ruinrd by too much seasoning. A good way to counteract this is to put your seasonings in a small muslin bag and take them out of the mix when the flavor is just right.
The fruit (or veggies or nuts or herbs or whatever) should be frozen, lightly cooked or choped/crushed before adding to the mix. With berries and the like it is easiest to just freeze them. Larger fruits can be chopped and fruits that are less juicy (apples or pumpkin) can be slighty cooked. This is done to release the flavors trapped by the skin of the fruits and make the juice go into the vodka more readily.
Once you gather all of your ingredients, basically you put them in a sterile airtight jar, shake them once a day for two weeks, let them steep and then strain them and let them age. Below is the pumpkin pie cordial recipe that I made.
Take one pie pumpkin, cut it in half and seed it. Sprinkle a liberal amount of store bought pumkin pie spice (~1/2 tbsp) on the two halves and microwave until pumkin flesh is soft.
After the pumkin is cooked, scoop out all of the flesh and put it into a sterile wide mouthed canning jar. Don't jam it in tight, just fill the jar loosley. Add one cup of white sugar and fill to the top of the jar with vodka. Store in a cool dark place.
Every day for two weeks shake the jar to resuspend the sugar. You don't need to really shake it hard, just get the sugar off of the bottom of the jar and mixed into the vodka. After two weeks you should not see any more sugar on the bottom of the jar. If you do, keep shaking it everyday until the sugar is gone.
Once the sugar has all been dissolved, you only need to shake the jar every week for about a month to keep the pumpkin mixed into the vodka. After about two months, you should be ready to strain the pumkin off. You should taste the cordial before you take out the pumkin to make sure that you have enough of the pumkin flavor in the mixture. To remove the pumkin, pour the mixture through cheesecloth or a fine mesh strainer into a new sterile jar. Squeese the pulp to get all of the juice out. Your new liquid will be cloudy, but that is okay because we will take care of that later. The pumkin you just took out can be discarded, or you can use it in your cooking. It will have lost some of it's flavor and will proabably look discolored, but taste it to see if there is enough flavor left. If there is, use it for pumpkin bread or cookies. The alcohol will all cook off and the final baked good will be alcohol free, but this way you get two uses out of your pumpkin.
Let the cordail age for about two months to make it more mellow. You should keep tasting it every week to see how it is progressing. Once you get it to where you like it, strain it again through cheesecloth to remove all of the particles. If you are careful and don't shake it up too much most of the particles will stay at the bottom of the jar where they settled. Now you can bottle it and share it. Some cordials have a pretty short shelf life and some are more durable. Mine was good for a couple of years without refrigeration. Some become undrinkable after a few weeks. You can always keep them in the fridge or in a cool dark place to make them last longer.