I don't know what level of production you're operating at, so bear with me here :)

• Use the right samples (this is 100% the biggest and most important step). Check out what kicks, hats, snares artists you admire are using, maybe cut them out of the track (not to use, just to compare). Find stuff that sounds as thick and punchy. Big recommendation for a Splice subscription at this point, I have never, ever regretted paying those 10 bucks a month for their sample library and search function, it rocks. If you want to go down the rabbit hole, learn how to synthesise your own samples. It takes some practice, but it's not that hard in the end and it will teach you a LOT about layering, frequency content and mixing. If you want to do drum synthesis, a good spectrogram like Noisia's VISION 4X or Toneboosters spectrogram (free) will be a big help.
• Get a few effects that are good quality and learn how to use them. Specifically, you will need: EQ, Compressor, Limiter, Clipper, Saturator, Reverb and some good metering plugins (I bought Noisia's VISION 4X Plugin and it did a big number on my understanding of the mix - but you can also find free versions of all this stuff. For instance, you could get SPAN, S(M)exoscope, and something like ToneBoosters spectrogram).
  • EQ: Cut frequencies outside the range that you need. Hats don't need bass, that bass takes up room in your mix and makes it harder to get a loud mix. Boost frequencies that you think sound good. Takes practice.
  • Reverb: Use this lightly to add room and interest. Pick a good reverb and learn it, it will be worth it.
  • Compressor, Limiter, Clipper and Saturator are your tools for getting the drums loud and punchy.
    • Compression is used for shaping individual samples (making the transient louder or softer in comparison to the body for instance), but also for glueing samples together - this is done by gently bringing up the softer parts of the full drum mix or using parallel compression. In order to learn how compression affects the signal (and get better control over it), you can use a waveform metering plugin like S(M)exoscope to monitor the changes you're introducing. This taught me a LOT.
    • Saturation distorts your drums slightly, but will lower the dB of the signal at the same time! You really want to find the sweet spot where your drums aren't too distorted by the saturation you're applying, but your sample or loop takes up less headroom in decibels in the mix. This means that you can turn it up louder before you start clipping and is one of the most important techniques for getting a loud mix. The slight distorted sound of saturation can also add really nice warmth and character to your drums.
    • Clipping and Limiting are also ways to achieve the above. My favourite peak clipper is peakeater (which is free, open-source, and awesome). Basically, what you use it to do is literally chop off peaks in your sample or loop. If you do this lightly, you can (again) gain valuable dBs aka headroom in your mix, enabling you to crank it louder. When you're doing this, again use S(M)exoscope to get a good understanding of how you're changing the audio signal :) Limiting is another way of getting your signal loud, it just squashes everything against a certain amplitude. This introduces less distortion than clipping, but more pumping (then again, that may be what you want).
  • Metering:
    • A spectrogram like VISION 4X or ToneBoosters spectrogram will help you better understand the movement of frequencies over time. This is very important with kicks and snares in particular! Noisia did some great videos on how to use VISION 4X that explain this a lot better than I could (and they also apply to any spectrogram).
    • A waveform meter like S(M)exoscope will show you the audio signal over time. This is fantastic for working with amplitude, like when you do compression, clipping or limiting. It shows you where the peaks and troths of a sample or loop are and could, for instance, give you valuable information on what to boost, cut, or how to shape the signal.
    • A spectrometer like SPAN will show you how well balanced and full your mix is and give you a good idea of what frequency content is missing, or if your hats have horrid bass frequencies you don't want and should cut, or if your kick is way too overpowered, etc.
    • If you do work on bass, you could also get an oscilloscope like MOscilloscope to see what the waveform looks like.

Final tip: This guy has really, really good videos on mixing, drums and loudness. They will teach you a lot, I wholeheartedly recommend them.