Imagine a vast land of seemingly endless plains and plateaus, stretching out for thousands of miles. The south being mostly open steppes, changing into an ever more densely forested landscape as you travel north, and eventually ending in tundra bordering on the northern coast. Impressive mountain ranges of the Caucasus run along Russia's southwestern border with Georgia, featuring Mt.Elbrus (5642m), highest mountain of Russia, and of Europe for that matter.
Further east are the mighty Ural mountains running from north to south across the country, marking the border between European and Asian Russia. Beyond are more plains until you reach the Siberian plateau in Russia's far east. To the south the Altai mountains rise up, followed by a whole series of less well-known but equally awesome mountain ranges from west to east, until you reach Lake Baikal, the world's deepest freshwater lake.
And this isn't all. Continue northeastwards from Lake Baikal to encounter still more mountain ranges with mysteriously ringing names like Synnagyn, Stanovoy, Verkhoyansk, Kolymsk, Cherskogo and Dzhugdzhur. Then at last, you will look across the Sea of Okhotsk, towards the Kamchatka Peninsula with its volcanoes and geysers, and south towards the island of Sakhalin and Primorski region.
Although the Russians themselves tend to be hunters rather than hikers, there are obviously great opportunities for long distance hiking in Russia. There are numerous trails in the Caucasus, Karelia, the Ural mountains, the Khibiny (northern Ural) mountains located north of the polar circle, the Altai mountains, Kamchatka, and in the Siberian taiga. Also there is the Great Baikal Trail planned to fully circumvent Lake Baikal. It is still under development, but over 500km is ready.
Russia's climate is decidedly continental. Spring and autumn are very brief, summers are very hot and winters extremely cold. However, be prepared for sudden weather changes and drops in temperature even in summertime. Of course climate in the polar regions is arctic: mild summers and freezing cold and dark winters.
Keep in mind that remote areas in Russia are true wilderness, and trails are generally not marked if visible at all. Reliable maps and documentation are hard to come by, non-existant or in Russian only. Mountain huts are an exception and very basic. Villages can be many days hiking apart, so you will need to carry compass, camping gear, clothes, food and sometimes water for several days. It can be risky to venture out on your own. It is not uncommon to hire a local guide. Ascending some of the higher mountains such as Mt.Elbrus may require a special permit. In short: hiking in Russia can be truly exploratory, and all the more adventurous.