Don't rush through the areas, look in every corner and behind every brick, and you'll be richly rewarded. It's the game's intention to make you explore the world. Alternatively boost them to 40 at least, so you can pick locks with the aid of a skill magazine that gives you a temporary 10 boost. Get your Science and Lockpick up to 50 as soon as possible, which allows you to pick locks on all average level locks and terminals.
Use V.A.T.S to greatly conserve precious ammo. If you're in need of healing, do it properly and rest.
They will greatly increase your self-sufficiency during your wasteland travels, and might even prevent you from dying! Definitely read this before your first playthrough, even if you're not planning to use the walkthrough. Save yourself the trouble and read these tips once or twice.