It's a tiger salamander, Ambystoma tigrinum sp.
You don't want any heat lamps on it or you can bake it to death or dehydrate it.
Looking at the picture, the salamander appears to no longer be in the neotenic (larval) phase of life (the gills behind the head have receeded from view). It's now in the terrestrial stage.
Tigers are big salamanders when they reach full size (8-15 inches in length). You are likely to want to start with a 20 long or preferably a 30 long aquarium. Some people who keep tigers prefer 40-55 gallon long tanks. You will want a secure screen top. If keeping the humidity up is a problem, use plexi-glass to cover 1/2 or 2/3 of the top making sure to leave enough visible screen for air circulation.
Salamanders, such as tigers do best in cool conditions - not hot or overly warm. Room temperature (60-75F) is best for them (tigers can also tolerate colder temps for short periods of time too so winter time is usually not a big deal to worry about).
They don't need special lighting like UVB. Just the light coming in naturally through the windows is fine (but don't stick a tank next to a window where the sun can shine into the tank - the glass can create a greenhouse effect and get too hot)
You want a terrarium style setup, fill it with several inches of loose forest dirt and leaf litter, etc. kept damp. Have some lightweight bark pieces for hiding spots. Expect some burrowing and digging by the salamander too, which is why lightweight objects are preferred...dont' want anything heavy to fall on top of it. The tank should be misted daily and if the soil dries out too much, dampen it again. You just don't want a bogged down tank of dirt that is full of water.
You want a shallow water area. Take a medium size 8" or so flat-side (not slanted) dog water dish or something similar (like the container in the photo) and bury it in the dirt leaving the upper lip free so that dirt doesn't spill into it too easy. Have a smooth rock or something in the dish to allow the salamander to easily climb out. It is important that amphibians not be put in contact with straight out of the tap water that contains chlorine/chloramimines. You will need to treat your tap water before using it around the salamander. Any standard water treatment product such as AmQuell used for fish water will work. I use old gallon size milk jugs filled with water and labeled for "Amphibian Use Only" (to keep people from thinking it's ok for people to drink). I will put some of the treatment liquid in, fill the jugs up with water and let sit over night before using. I often keep several such jugs full and ready to use at a moment's notice that way I don't have to scramble around in an emergency if I have one jug empty. Water in the water dish should be changed regularly to keep it fresh. Likewise, make sure the water you use to mist the tank is the treated water.
Stock the dirt in the tank with a good supply of earthworms and nightcrawlers. That will deal with any snack time hunger issues the salamander might have. Also you can feed crickets, but you never leave them in the tank for more than an hour... always supervise to make sure the salamander eats them..remove any uneaten ones. Crickets can chew on the soft skin causing skin lesions and infections.
About every two weeks, take objects out of the tank and stir the dirt and leaf litter up to aerate it and to take note of how many worms are left and whether you need to restock again. Don't bother using live plants in the tank cause tigers will just walk all over them and trash them. Every 3rd month, replace the dirt in the tank with new dirt. Pick out the worms from the old dirt to put back into the tank.
And congratulations on the new baby. They regularly live 15-20 years in captivity with minimal attention needed as long as their basic requirements are met. 
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PHWyvern
