Your first mount will be a very slow wolf, by leveling you are getting some temporal mounts, so after a while they disappear.
If you have a guild and/or friends you could ask them for the Viverne, that drops at the enboss of OBS or can be purchased in Alrihat.
Other option would be the Allods Shop and buy the Lightning Bolt's Keychain (P2P) for 7 Euros
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In Nezeb (Vladimir Kostin) and Novograd (Ivan Ovsov) you can find an NPC that sells mounts and pattern.
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You can get mounts by doing old raids:
Lv.51 Dead City/ Cradle (Dragon way, last boss) - Gryphon
Lv.55 Tep's Pyramid/ Irdich - Magic carpet
Lv. 60 Eclipse/ Umoira - Dragon
Lv. 65 Gates Project/ Laboratory / Negus Jeeg (go in with another person to help with this boss) Ferris - Wraith (has a "blink" too)
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You can get mounts from Prophetic Cards (temp. Events) , Observatory, Nihaz Citadel , on Astral Allods and some NPC's (Alrihat, PVP NPC, 3v3 NPC, Dionic Ammer NPC etc.)