I like my teas on the mellow side as well. Unfortunately I think we are in the minority. It seems like bitter is what most people are looking for when they brew tea. We are Sangrias in a Beer world.
For a weaker tea you could brew it for a shorter time or just use less. If you are new to tea you're probably having it in the bag so using less won't really apply.
Brewing for a shorter period will definetely make for a mellower tea. I love a good Assam but find it tastes best at about 3 1/2 minutes for me. Basically tea (loose black) has a brew life cycle of:
[:?] 1-3 minute = weak tea
[:)] 3 1/2 to 4 1/2 minutes = normal to strong tea
[:shock:] after 5 minutes = getting bitter
This is for loose tea but if it's bags you're using the times are much shorter but follow the same basic pattern.
Black tea needs water that is boiling to get the good stuff out of it and into your cup. If you brew it at a lower temperature it has a different flavor - less robust but not necessarily in a mellow way.
The other option mentioned, using less tea is also an excellent way to get a mellower brew. This has the added benefit of making your tea last a little longer.
Bonus Answer: I find the best cup is usually the second one brewed from the tea. I felt like a real cheapskate the first time I tried this but it really tasted better than the first. Just brew it for about 30 seconds longer. It'll be about as mellow as it gets but have all the flavor you want. First cup to wake up. Second cup to enjoy.