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Fallout Wiki
At the base level, you need 1300 skill points for complete maximization (100 points for 13 skills). At level 1, you get 45 skill points for free (from your 3 Tag! skills), and an average character (5 in all SPECIAL stats) will have 15 as a base for all skills. This reduces the amount of skill points you need to 1060 (1300 - (45 + 15 x 13)).
For 49 levels at average intelligence, you get 612 skill points (12.5 x 49). Just with these base stats, this is enough to get all but 6 skills completely maxed out (remaining 448 / 85, rounding up).
Simply by taking Educated at level 4 leaves us with 356 skill points remaining to completely max out. Taking Comprehension at level 6 (and saving skill books until then) means that reading 89 skill books is enough to net you the remaining skill points (so long as you adapt your per-level skill points to the remaining skill books). As a note, the base game contains 53 skill book; Old World blues contains 16 skill books/recipes; Dead Money also contains 12; and Honest Hearts can contain anywhere from 0 to 8, 0 to 2 per workbench (and may require a bit of saving and reloading before entering caves). With diligence in finding skill books/recipes (all well-documented on this wikia) and a bit of reloading in Honest Hearts to generate all 8, you can max out all skills without any other special character effort.
A character with Intelligence of 10 with Educated at level 4 and starting off with Skilled will be short only 408 skill points, not including skill points from initial character creation (which will yield at least 111: 45 from three Tag! skills and 22 from Repair/Medicine/Science, ignoring Luck). This character will need only very few skill books by comparison, about 42 if all other SPECIAL stats are left at 5.