Modifying a campaign for 2 players?

I'm relatively new to D&D and DMing in general, but have picked up the new 5E starter set to play with one other player. Does anyone have tips on how to adjust the difficulty for this as opposed to running it as a 5p campaign as is intended? Thanks

Hmm... I assume you have 2 players and a DM. The DM should probably look through all the encounters and either cut the number of opponents in half, or cut all their hit points in half. Also, if one of the players is not a healer of some variety, he'll want to give them several healing potions to start out, and probably supplement some of the treasure with healing potions or other healing/damage mitigation things. Low level characters are already pretty easy to overwhelm, and your DM will want to be careful not to outright crush either player with too much damage. You might consider each playing 2 characters as an easier alternative to rebalanceing, but if the DM is careful and always has an out for the players (make monsters more likely to run away, or negotiate, have a Deus Ex Machina NPC waiting in the wings in case the tide turns, fudge the dice, outright lie. =D), it should go fine.

Let the players have a few npc's to boss around. Those npc's could be used to fill any hole you have in the group. Say both players want to play thieves then give them a couple fighters and a cleric or if one wants to play a magic user and the other wants to play a fighter then throw another npc fighter, a cleric, and a thief into the mix. Let the players lead the party and decide on their combat actions. This will give them extra characters which was suggested above but lets you control how the party is filled out.

I believe he is talking about 1 DM and 1 player. Just do like Aaron said.

If you plan to run your own adventures (from your imagination) then it's quite easier to DM for any number of players, based on my experiences with both official Modules, versus my own homebrew campaigns. I regularly DM for 1 player alone, or 2 players (or any number from 1 to 9 players). If you have questions for how to make up your own adventure ideas for 2 Players, just ask, and I can help with addressing that question separately. If you plan to run the published adventure that's in the 5E Starter Set: definitely use some techniques like what Aaron and Pat have suggested. Their replies are already packed with good methods, and most of what I can say is paraphrasing what they advised. Like the original post asked, you can call this modifying, or adjusting --- another common synonym or related term for this is "re-scaling" so you can scale or re-scale the encounters to fit the Players that you have. You can scale the number of monsters, or the hit-points for each monster, down. That's pretty obvious but I don't know if it was mentioned yet. If you really mean like Specter interpreted this --- 1 DM and 1 Player --- then my advice is to let the 1 player run a whole party. One player alone can control 3 or 4 PC's (or up to 6-7). Or the Player can "be" their one PC who is a leader, and all the others are Henchmen-Followers (perhaps some controlled by the Player and some by the DM). It changes the dynamic of the game a lot, and is very fun, if the DM and player are friends & can be patient and proceed at the appropriate pace when 1 player has his hands full with a line of character sheets laid in front of him.