Trust me it is really quite easy ...
Spend 15 minutes learning the basic bits of the LR interface ...
The Lightroom catalogue is a list of images, where they are physically stored on your computer, what collections they belong in and what edits to apply to them. Each bit becomes clear with use and as you understand more and is worth persevering with. You can one or more catalogues too, but you can worry over that later, first up just use one for now.
If it helps, my typical work flow using LR goes like this. I'm assuming very little LR knowledge so if I'm teaching grandma to suck eggs, I apologise!
After the shoot I plug the memory card from the camera into the card reader (you can use the usb lead from the camera too). In LR choose the import function, you may have to select Library first to get to this (upper right hand corner of the LR work area). On the left is the source panel, this is where the pics are coming from, usually it will have selected the memory card. Middle top of the import screen you have choices as to how you import (Copy as DNG, Copy, Add and Move). 99% of the time I use Copy. The really useful bit is in the right hand panel, this is where you tell LR where and how to add files. I always use the rename files option, usually will put something like the shoot name and possibly the camera body it came from. In 99% of times I use the Custom Name - Original File number option as the Template for this. So an example name would be belgium_discus_show_D600 and when a file is imported it will have the name something like belgium_discus_show_D600-5067.nef. I also always use the keywords option, you can put what you like here, keywords are synonymous with tags and make searching very easy. e.g. for the above file I could use Belgium, D600, Discus, Show, 2013 (note they are separated by commas).
I always allow LR to organise where the files are stored once I have setup the root folder - only do this once btw not each time you import - allow LR to do the heavy lifting, it is good at it! I use organise by date.
Renaming the files is useful particularly if you need to find the files on your hard disk outside of LR, the keywords allow easy searching (they have other uses too).
You can apply a variety of pre-sets on import such as some develop actions, copyright data and other meta data changes. There is plenty of help on the web for this when you need it (you will too at some point

).
Once imported you can then use the Library features to organise your work. The nice thing here is you can do this in many ways and have the same image in many collections. The left panel is where you do this. It usually has the following sections, Navigator, Catalog, Folders, Collections, Publish Services. Under the Catalog section the most useful (to me) option is All Photographs, this is where I usually start if I'm looking for a particular image or type of image (the keywords work well for this).
The best part of LR in terms of organisation is the Collections. You can create as many as you can then add images to the collection, e.g. you could have one called Family or Pets etc ... or if you have just shot an event something like Pompey FA Cup

The good thing here is that the physical image file remains where it was imported too, in fact the same image can be in many collections.
All of the above information is stored in the LR catalogue. Don't confuse this with the Catalog section in the Library as that is basically just a list of photos. When you use the other modules of LR, i.e. Develop, Map, Book, Slideshow, Print and Web, any changes you make here are also stored in the LR catalogue. An important point here is LR is non destructive, that means it never alters the original file (other than file name and meta data changes). Instead it records any changes you make as a series of actions in the LR catalogue and when you open the image in LR it re-applies these changes. It also applies these changes on output.
As you see every action you take in LR is stored in the LR catalogue, the nice thing is that it is extremely difficult to nigh on impossible to any damage to your image files using LR. LR is almost an all or nothing solution, if you "buy into" LR then use it for all image organisation as it makes life much easier imo/e - believe me the above only scrtahes the surface of what it can do.
I do take other actions during import, such as archiving etc but these are outside of LR.
Hope that helps.
EDIT: I should also add this is the way I have come to use LR, it isn't the only way!