There are 2 kinds of Portals: Nether Portals and End Portals. A Nether portal is created by placing obsidian in a 4x5 pattern then lighting it on fire using flint & steel. Once lit, the inside of the portal will turn purple and begin moving. When you step inside a portal, you are teleported to the Nether. To re-enter the over world, simply step back inside the portal.
End Portals can be found in strongholds, which spawn naturally in the over world. Although very rare, by right-clicking while holding an eye of ender it will fly off in the direction of the fortress. Once found, you must search through the fortress until you find the End Portal. Once found, you must place eye-of-enders in the holes and then a portal will open which takes you to the End.
Related ThreadsBeware the Portal Trap - last post by @ Jul 19, 2014
Can I mine an End portal frame? - last post by @ Mar 29, 2015
Nether Portal Questions - last post by @ Jul 2, 2012
No End Portal in my fortress...deets below. - last post by @ Aug 4, 2015
Minecraft/Portal Affinity? - last post by @ May 23, 2011