Try turning the headlights on, and then walk around so you can look at them from the front. If the headlights do not work; then there is either a corroded or bad connection in one of the battery cables, or the battery has failed (which sometimes happens with new batteries), or you left the radio or an interior light on and it drained your battery (in which case you'd need to get the battery recharged), or someone has stolen your new battery.
If the headlights are as bright as they usually are; then there is either a problem in the starter, or the starter solenoid, or the neutral safety switch, or the ignition switch. Try to start the engine when the transmission lever is in neutral. It normally should be able to start in either neutral or in park; but sometimes the switch goes out of adjustment, and it then will only start in neutral. Sometimes the gearshift lever just has to be moved a little, and then it will work.
If none of these techniques work; then you'll need to get someone to check the starter, the starter solenoid, the neutral safety switch, and the ignition switch.
I hope this helps!!!