Fighting Style Protection (not really recommended, but should be mentioned)
The easiest thing to protect someone as a low-level 5e Fighter is the Fighting Style Protection (PHB p. 72).
Protection basically gives you the chance to impose Disadvantage upon an attack roll against a creature that is not you, but within 5 feet of you, though you need to have a shield in one of your hands for this Fighting Style to work.
This means your fighters need to choose this Fighting Style on level 1, both have a shield and stand right in front of the Wizard. Furthermore it limits you to the reactions of your Fighters, meaning you can use this only once per Fighter and they can't use their reactions to use for example Opportunity Attacks. All in all not a great option in your specific scenario, but the closest you will probably get with level 1 characters. Though running into 10 Goblins at once with only 3 level 1 characters would probably be a Deadly encounter and you should try not to go into an open fight like that.
Keep in mind that the Protection Fighting Style is not really a good option in general. Most people would say that it's pretty much useless as a Fighting Style. Be careful when choosing this Fighting Styles, but I think it's important to at least mention this option.
Use the terrain, Luke!
For completeness: One of the easiest things to do after this is probably to use the terrain. Place the Wizard with his back to the wall and make sure that there is no way around the Fighters to get to the Wizard. Use doors to make sure the Goblins can't go around. Stand on top of a ledge. Place the Wizard behind a stalagmite. Hide behind the corner and ready your actions. Distract enemies and try to get behind them. Get them apart in different rooms of the cave. Hide in the shadows. The options are near endless hear and only depend on the imagination of you and your DM. This gives you the most advantage. Especially on low levels it's incredibly important.
You mentioned a large open space so this is not possible in your specific scenario.
Level 3 gives your Fighters access to the Battlemaster Archetype (PHB p. 73). This means they get special maneuvers they can use. These maneuvers might help a bit, but the sheer mass of enemies will be a big problem. Useful maneuvers include Goad, Maneuver, Menace and Push. You have to choose which maneuvers you think are most useful for you learning 3 at level 3 and getting 4 superiority dice. All maneuvers can be found on PHB p. 74.
Goad basically gives you the chance to force a creature you damage to make a Wisdom Saving Throw and impose Disadvantage on their next attack against any target that is not you until the end of your next turn.
A single enemy gets Disadvantage. Disadvantage will be very helpful to survive the next attack from this enemy. But only one enemy and only one attack and the enemy has to attack your Wizard.
Maneuver gives you the chance to make an ally move up to half their speed using their reaction. Furthermore your chosen ally won't provoke opportunity attacks.
Help your Wizard friend to move out of reach of the Goblins. Arguably they can catch up on their next turn again, but your Wizard can more easily position himself with your Fighters help.
Menace makes the target of your attack frightened until the end of your next turn if they fail their Wisdom Saving Throw.
If the enemy is frightened they can't get close to you and by keeping your Wizard friend close to you the enemy can't get closer to your Wizard friend. You should keep in mind that the enemy can still attack the Wizard from a distance and that "getting closer" might not be very useful if you already attacked them in close-quarters combat.
Push gives you the chance to push an enemy such as a Goblin up to 15 feet away from you.
Pushing the enemy away might stall their progress a bit.
All in all these maneuvery are all not really useful with the amount of enemies you proposed. Those numbers are just too high.
If your fighters are level 4 and they are allowed to choose feats you should have a look at Sentinel (PHB p. 168/170).
Sentinel basically gives you the chance to reduce the enemies speed to zero if you hit them with an Opportunity Attack, make an Opportunity Attack even if they are trying to Disengage and make an Opportunity Attack if the target is in your melee range and trying to attack someone who is not you and doesn't have this feat.
This is probably the best feat for what you want to achieve. It depends on whether you still count this as low-level or not, but if your Fighters have access to this feat they can reduce the enemies speed to 0, get a drop on the enemy even if those pesky, nimble Goblins use their Bonus Action as a Disengage Action and protect your Wizard if they stand in melee range of the Goblins. Of course this is also limited to the reaction of the Fighters and might therefore not be sufficient for a horde of 10 Goblins.
Early level Wizard spells to increase survivability
For the Wizard I recommend Color Spray (Level 1 Illusion which basically allows you to blind creatures in a 15-foot cone for one round. Depending on the positioning you might be able to blind quite a few enemies for one round.
Shield is also quite useful for not dying as it allows you to increase your AC by 5 until you start your next turn when you are hit by an attack.
Later your Wizard gets access to spells like Blur to increase his survivability, which imposes Disadvantage on attack rolls that are made against you.
TL;DR; All things considered you don't have a lot of options if you are facing a high amount of enemies like 10 Goblins with only 3 Level 1 characters and even on level 4 your options are limited at best. You should try to avoid encounters that are this much in the favour of your enemies. Use the terrain and try to fight only small groups. Use surprise to the best of your abilities. Otherwise a bigger group will kill your party.