Disclaimer I don't know how much of any of this you already know. It is not my intention to come across as insulting or condescending, but to provide as much information as practical.
Put the camera in manual mode, or one of the priority modes (aperture priority or shutter priority). These are the most "no-frills" modes you can get on modern cameras and leave most or all of the responsibility for setting the camera up to you.
The camera will likely have a metering display inside the viewfinder or on the rear LCD screen (likely both, if it has a rear screen). This tells you if, with your current camera settings, the scene will be over or under exposed compared to how the camera has metered the scene. If you use aperture priority or shutter priority, then instead of indicating over or under exposure, the camera instead lets you set either just the aperture or the shutter speed and will automatically adjust the other variable to get the exposure that the camera has metered (there's usually also an option to tell the camera to specifically over or under expose by a particular amount).
Also on the topic of metering, most modern cameras have multiple metering modes. You're probably already familiar with spot metering and center-weighted metering, but cameras typically also include something called "evaluative" metering (or another manufacturer-specific term). With this mode, the camera uses a computer algorithm to decide what the best metering is. Although it may give better results for novice users, most serious photographers avoid it because the results do not follow any predictable rules and are based on the manufacturer's programming. Set the camera to spot or center-weighted metering according to whatever you're more comfortable with.
Regarding focus, cameras typically do not have split prism viewfinders anymore (although I believe some third-party companies are offering a service to retro-fit particular models of cameras with split prism viewfinder screens). Most of the time it is expected that users will use autofocus mode. In this mode, the user selects one of a predefined set of points in the image which the camera will automatically ensure is in focus before taking the image. The camera will likely also have the option to focus using whichever point it prefers (again according to an algorithm decided by the manufacturer) and an option to track and "anticipate" focus during motion shots.
However it is possible to set the camera to manual focus mode and in this case the camera will indicate if the image is in focus (with a small margin for error) but will not perform any focusing by itself. Admittedly manually focusing an image in this way is somewhat difficult and most of the time I only use manual focus if the camera does not manage to focus correctly (e.g. bad lighting, awkward subject) or to make small adjustments to the camera's focus. I also tend to switch to manual focus mode right after autofocusing if I'm shooting multiple images without changing the scene, to prevent the camera from re-focusing and messing up the image.
The other main differences that you'll encounter with digital cameras compared to film cameras is ISO and white balance. Whereas with film these are both determined by the film that you put in the camera, digital cameras let you change the ISO on a per-picture basis (more on white balance later). Most modern cameras will have an option to change the ISO automatically to get the correct exposure (giving the camera a second variable to adjust when shooting in aperture or shutter priority mode), but this is often annoying and can lead to unpredictable results. Many photographers prefer to set the ISO manually and then leave the camera to adjust just the shutter speed or aperture. If you're coming from film, you'd probably want to set the ISO to match whatever film you would have used for an equivalent situation/environment/lighting/scene.
White balance is handled a bit differently with digital instead of film and explaining this first requires explaining what raw images are. Any DSLR should be able to take what are called "raw" images, which unlike a JPEG image cannot be displayed directly by a computer. Instead, these images capture exactly the data that comes out of the image sensor in the camera, and need to be post-processed to produce an image file that you can view. Raw images are a bit like the image that you get on film before it's been printed onto photographic paper, and post-processing them is a bit like doing your own printing but without the inconveniences.
The camera should have an option to choose which format to save images in, and you should use raw format because this gives you the ability to process the photos to your own liking. By contrast, if you choose to save the images in JPEG format then the camera will automatically post-process the photo (again according to a manufacturer-decided algorithm) and you won't really be able to process it again yourself. (When you use raw format, the camera will still post-process the photo to display on the LCD screen if it has one, but the data that you get off the SD card is the raw image and once you've post-processed it it need not look anything like what you see on the camera's LCD.)
However, unlike film, when a digital camera takes a photo the white balance is determined at the post-processing stage rather than at the capture stage. The sensor in a digital camera has no concept of white balance, just different amounts of light hitting the sensor. So with digital, you'll set the white balance during post-processing. This has the added advantage of letting you change the white balance later on. The camera will likely still have an option to set the white balance (including, as always, an "automatic" option) but this only applies to the preview that you see on the LCD screen and if you've set the camera to save in JPEG format - if you save in raw format, it doesn't affect what you finally get.
TL;DR Use either manual mode, aperture priority mode, or shutter speed priority mode on the camera. Read through the manual and disable any other automatic features that you don't want. If you want better control over the final result, use raw image format and post-process the photos yourself.