You've spent a lot of time with your old camera, but everything was auto. Now you have a dSLR in your hands, and the options are overwhelming. You want to use M (Manual), but isn't there a way to baby step into it? Yes.
You can start your transition with A (Aperture priority) or S (Shutter priority). Aperture controls how big the hole is that lets light into your camera. Bigger number, smaller hole (think of it as a fraction, and the number you see is the denominator). So an aperture of 5.6 is letting in lots of light, and an aperture of 36 is letting in only a tiny bit of light. Bonus - aperture also controls your depth of field. Do you want ALL THE THINGS to be in focus, #anseladams? You need a bigger number. Do you want only one thing in focus, #portraits? Get a smaller number and prep for pretty bokeh in the background.
Maybe you don't care about depth of field. What you care about is capturing motion, and shutter speed is your tool of choice. Cool. Larger numbers mean faster shutter speed - 500 means 1/500th of a second. Are you looking to purposefully blur your images, #aftermyownheart? Slow your shutter to 1/10 or slower. I've used 10 second exposures on the highway (I wasn't driving, promise), 1/3 second for koi splashing around, and 1 second for walking texture images. Play!
High ISOs mean noise in your image, so I aim for super low ISOs (400 or less). If you've set your ISO to auto, check your images every so often to see what you're getting. If your ISO is over 400, give your images more light to get that number lower.
With me so far? Good. A few more:
I use auto-focus as much as possible. What if your camera wants to focus on the center of your viewfinder, and you want to focus on something in the corner? Move your corner subject to the center, press the shutter halfway to focus, then move the subject back where you want it and press the rest of the way. That should keep the object of your desire focused. Want to focus on something super close, and your camera is just obsessing about the background? Try manual focus. If that doesn't work, you might just be closer than your lens is capable of focusing. Move your feet to fix that.
5. Watch Your Borders
Borders can separate a decent image from a good image. If you've found something worth shooting, check the image after you shoot, and let your eye circle the border edges. Is there anything distracting? A bright spot, a dark spot, a smudge - anything that distracts from your subject? If so, reshoot the image to remove that. (Or worst case, remove in post-processing.)
Where is your light source? In front of you, giving you a backlit subject? Behind you, giving you a front-lit (#boring) subject? Straight to the side? You can do a lot with light - do it on purpose.
Remember the rule of thirds, then remember that rules are meant to be broken. (But don't think you can break a rule you never learned as well as someone who learned the rule then broke it.) Look for triangles, patterns, and don't decapitate.
What's most helpful to you?