On the left side, you will find a Button called "No mech selected" or with the name of the current loaded variant. Clicking on that button will open a menu, from which you can select any available variant and load it into the mechlab. By default a completely empty mech will be loaded. You can use the "Tools" Button -> "Load stock loadout" to load the Stock loadout of the selected variant.
To put new weapons or equipment to your mech simply drag and drop the items from the equipment bar to your mech. The equipment bar is separated into 3 tabs (like in game) for weapons, ammo and modules/engines. There is also a quick filter for weapons and modules/engines.
To remove items from your loadout you can drag and drop the item back to the equipment bar, or click the X icon in the slot. To remove all items from the mech, click the "Tools" button and select "Strip mech"
After selecting a mech from the menu you start with a completely empty mech, to add armor you can click the + or - buttons on each component or use "Tools" -> "Max armor" and then adjust the armor values manually.
After you finished your loadout you can click the "Save & share loadout" Button to permanently save your loadout. A Popup will appear in which you can copy the unique url to your loadout. This url can be bookmarked or shared.
If you are registered, you can add your saved mech to the mechbay. In the mechbay itself you can see a quick overview about the mech. A click on the name automatically loads the loadout to the mechlab.