The Forge comes with an automatic installer; when you run Forge, make sure you select "client".
When the Forge installation is done, open the new Minecraft launcher and click "Edit Profile", and a pop-up window should appear with lots of settings. Then go down to "Use Version" and click on the drop-down menu. There should be an option called "release 1.7.10-Forge10.13.0.XXXX" (with the X's being four numbers. Choose that and click "Save Profile".
If Minecraft loads without crashing then you have installed Forge correctly.