You're basically rotating it into place by starting at an angle, which is the key to getting it to seat properly. You should feel it snap into place. If it doesn't, check to make sure you have everything lined up correctly and try again. If your slots have clips, sometimes they'll close during a failed attempt to install a module and will need to be reopened on your second attempt. It does take some pressure to get them installed properly.
Some manufacturers recommend different methods of installing DIMMs.
If your computer's manufacturer recommends a different method, it's best to do it that way. When you have the RAM module in place, examine it from a couple of different angles to make sure it's lined up correctly with the old modules. If it appears to be sticking out too much, gently push on it until it looks right. If the slot has clips, they'll usually close automatically as the RAM module seats. Sometimes, however, you have to close the clips manually.