I asked the very same question before and the very kind XDgal gave me a lot of tips. So i'll share my part of stupid experience. Please note that I am not very handy and this was my first time.
Safety:
1. Wear steel toe boots - unless you think your toes are worthless.
2. Get some good gloves
3. Good eye protection - goggles
4. hearing protection - that thing is LOUD. Yes, the headsets/mufflers you use at gun range would do.
5. Watch your legs and arms - when you put pressure on the drill, be careful not to bend the drill bit. You may break the drill bit and fall.
6. If you drill through carpet or wood, watch it so that it doesn't catch on fire
Tools and Gears:
1. Get a hammer drill!!! I tried to rent one but Home Depot wants too much money. I'll tell you, it takes a while to drill. So I ended up spending $80 and bought a top-of-the-line Bosch hammer till from ebay.
2. Ditch the lag screw and buy your own proper concrete anchors. Home Depot sells them and I bought the 1/2 inch ones.
3. Get a good masonry drill bit - again, I bought a Bosch from Home Depot for $12 (1/2 inch). I didn't go for the "diamond tip" one but I only had two holes to drill.
4. Vacuum and light at ready
Fun Part:
1. Cut the carpet out, if you can. Mine's about 1/2 wood floor. I was too lazy to cut the wood out.
2. Move the safe into its position and mark the spots from inside of the safe
3. Start drilling!!! I didn't not move my safe out of way. I just put my drill through the hole and started to drill from inside of my safe. My safe was very small but still gave me enough room to put enough pressure on the drill.
4. Take a break if you think the drill gets too hot
5. vacuum as you go
It took me 1.5 hours to drill 1.5 holes and another 30 minutes to finish another 1/4 hole, then I gave up.
Essentially you want to drill deep enough that in case you want to move the safe, you can just hammer the anchors down till it's flush to the floor. My anchors are 4 inches and I did 5 inches hole. In the process, as XDgal predicted, you would probably hit something really hard and the drill bit would stop advancing. Check the drill bit and see if there's any filing. If yes, you probably hit a rabar, you may want to try a different spot if your hole is not deep enough; if not, just keep on it and the hard piece will break.
On my first hole, the hard piece did break after about 15-20 minutes of trying, but on the second hole, I had to give up after about 1 hour, fearing that I might burn up my drill.
Either way it's a fun process and it helps if you can get the wife and kids out so that you have your house to yourself; otherwise the nagging/yelling would be worse than the drilling noise and harder to muffle or deal with.