Here is some general drill press advice for new people from a machinist.
1) Secure your part with either a vise or a clamp, do not simply hold the part in your hand. As soon as the drill breaks through the other side it could grab a burr, torque the part and spin or "helicopter" on you quickly.
2) Center punch or center drill the spot you're going to drill prior to using your twist drill. Otherwise the drill will "walk" and your hole will be eccentric and out of location slightly. You can mark the steel using a automatic spring loaded center punch and then follow that with a standard center punch to enlarge the mark.
3) Choose the correct speed (RPM) for the material and diameter for the drill you're using. To do this you need to do some research, the drill manufacturers or machinery's handbook will list suggested SFM / FPM (Surface Feet Per Minute) for their different types of drills and materials. To convert SFM to RPM's use this formula, SFM x 3.82 / Diameter of drill. For example 15 SFM x 3.82 / .125 (1/8 Drill Diameter) = 458 RPM, now choose the closest setting your drill press will allow. To change the speed on your drill press open the top sheet metal enclosure and adjust the belt to the corresponding diameters shown on the diagram on your drill press. For M42 Cobalt Jobber length twist drills which is the industry standard length, you'll generally be drilling in the 15-30 SFM range for annealed high carbon steel, tool steel and stainless steel. When in doubt start on the lower side of the suggested values.
4) When possible use a cutting oil it'll extend drill life and produce better finishes, do some research as different materials perform better with different oils. For most annealed cutlery grade steels
https://www.crcindustries.com/products/truetap-174-hd-heavy-duty-cutting-fluid-16-fl-oz-03400.html or a similar sulfurized oil product would be a good starting point. WD40 is NOT a cutting fluid / lubricant, it's only a protectant.
Hope that helps some, If you have any other questions let me know.